NORTHWESTERN UNIVERSITY MULTI-SPECTRAL RAMAN GAIN IN DUAL-ISOTOPE RUBIDIUM VAPOR A THESIS SUBMITTED TO THE GRADUATE SCHOOL

Transcription

1 NORTHWESTERN UNIVERSITY MULTI-SPECTRAL RAMAN GAIN IN DUAL-ISOTOPE RUBIDIUM VAPOR A THESIS SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree MASTER OF SCIENCE Field of Electrical and Computer Engineering By Joseph E. Vornehm Jr. EVANSTON, ILLINOIS June 2005

2 ii Copyright 2005 by Joseph E. Vornehm, Jr.

3 Abstract Multi-Spectral Raman Gain in Dual-Isotope Rubidium Vapor Joseph E. Vornehm Jr. An experimental system is presented for generating and observing Raman gain in neutral rubidium vapor. The development of a sophisticated, highly accurate detection system for spectrally resolved photon counting is described as well. Experimental results are given, including for both continuous-wave (CW) and pulsed excitation of the vapor medium. Most interestingly, in dual-isotope rubidium vapor, a single pump laser excites as many as eight spectral lines; these lines are explored through numerical simulation and found to correspond to Stokes and anti-stokes fields from each rubidium isotope, as well as shifted variants of these lines due to the AC Stark effect. A conceptual theoretical background is given initially, and a somewhat more detailed description of the theory is added later. Additional experimental details are included in several appices. The text is written to be largely accessible to readers with an undergraduate education in engineering or physics. iii

4 To Meta and Lili with love iv

5 Table of Contents Acknowledgements...xiii Chapter 1: Introduction Overview Properties of Rubidium Energy Level Transitions Three-Level Systems Rubidium D Line Transitions The Raman Effect Stokes Generation Anti-Stokes Generation The Stimulated Raman Effect Optical Pumping Applications of Raman Transitions Quantum Memory Quantum Entanglement Generation Other Experiments Chapter 2: Experiment Description Realization of a Raman System Phases of the Experiment v

6 vi 2.2 Phase I Raman Gain Initial Setup The Fabry-Pérot Spectrum Analyzer Phase II Experimental Refinements Single Photon Detection Glass Raman Cell Magnetic Shielding Phase III Pulsed Excitation Isotopically Pure Raman Cell Pulsed Excitation Using AOMs Glass Absorption Cell Photon Correlation and Photon Number Correlation Experimental Details Laser Frequency Generation and Tuning Vapor Cells Absorption and Filtering Phase I, II, and III Details Other Modifications Chapter 3: The Detection System Overview Spectral Resolution of a Classical Signal The Fabry-Pérot Spectrum Analyzer... 73

7 vii Neutral-Density Filter Wheels The Classical Photodetector The TDS 3012 Digital Oscilloscope Computer Interfaces Performance Spectral Resolution at Low Light Levels The Photon-Counting APD The SR400 Photon Counter The SR430 Scaler/Averager Pulsed Excitation and Pulse Control Pulse Generation Photon Detection Performance Computer Control of the Detection System GPIB LabVIEW LabVIEW Execution The Vapor Cell Experiment LabVIEW Program User Interface Data File Format VI Internal Structure Performance

8 viii 3.7 Computer-Aided Analysis Data Import Commands Plotting and Analysis RS-232 Instrument Control Chapter 4: Experimental Results Summary of Results Classical-Level Results Anti-Stokes Generation at Classical Levels Vapor Cell Absorption Spectra Spectrally Resolved Photon Counting Multi-Spectral Raman Gain Effects of Optical Pumping Isotopically Pure Line Spectrum Pulsed Excitation Chapter 5: Theory Raman Effect in an Atomic Ensemble Rabi Oscillations Collective Excitation Mode Entanglement Using the Raman Effect Photon Storage Using the Raman Effect Chapter 6: Conclusion Results and Validity

9 ix 6.2 Future Direction References Appix A: APD Power Supply Appix B: Fabry-Pérot Cavities Appix C: LabVIEW Documentation Appix D: MATLAB Source Code

10 List of Figures Figure 1. A three-level system Figure 2. Rubidium absorption spectrum Figure 3. Rubidium levels involved in D2 transitions Figure 4. Relevant energy levels for the present experiment Figure 5. Raman transitions Figure 6. A quantum memory experiment Figure 7. Energy level structure for a quantum memory experiment Figure 8. Heat pipe cell diagram Figure 9. Acousto-optic modulator (AOM) schematic Figure 10. Summary of the three experiment phases Figure 11. Phase I and II experiment diagram Figure 12. Relevant energy levels for the present experiment Figure 13. Heating coil wrapping Figure 14. Pulse timing diagram Figure 15. Energy level structure for pulsed excitation Figure 16. Block diagram of experiment Figure 17. Schematic diagram of Phase I and Phase II of the experiment Figure 18. Schematic diagram of Phase III of the experiment Figure 19. Saturated absorption spectrum for rubidium x

11 xi Figure 20. Relative shift between pump and probe Figure 21. Heating coil wrapping Figure 22. Magnetic shielding for glass vapor cells Figure 23. Location of polarizing beamsplitter cube performing primary polarization filtering Figure 24. Frequency spectrum used in Phase I and Phase II Figure 25. Frequency spectrum used in Phase III Figure 26. Typical absorption spectrum measurement Figure 27. Detection system block diagram Figure 28. High voltage ramp distortion Figure 29. Shielding for APD and fiber coupling lens Figure 30. APD gate switching circuit Figure 31. Fabry-Pérot ramp mirror image Figure 32. Pulsed-mode excitation timing diagram Figure 33. APD dead time Figure 34. Vapor Cell Experiment VI front panel Figure 35. Stimulated Raman gain, FSR of 15 GHz Figure GHz beat note between Raman anti-stokes line and probe line Figure 37. Saturated absorption spectrum for mixed-isotope cell Figure 38. Absorption spectra for three vapor cells Figure 39. Population transfer with optical pumping Figure 40. Single-photon, spectrally resolved trace showing multi-spectral gain

12 xii Figure 41. Stokes (probe) vs. anti-stokes intensity Figure 42. Light shift with increasing optical pump power Figure 43. Simulation results compared to experimental results Figure 44. Stokes and anti-stokes powers for different detunings Figure Rb spectrum with 27 GHz FSR Figure Rb cell lines Figure 47. Population decay after 0.5 ms optical pumping pulse Figure 48. A typical pulse, as recorded by the APD Figure 49. Pulsed-mode excitation Figure 50. A three-level system Figure 51. Hard drive and ATX power connectors Figure 52. Schematic of a Fabry-Pérot cavity Figure 53. Important locations for analyzing cavity resonance Figure 54. Transmitted light intensity for three values of F

13 Acknowledgements The author gratefully acknowledges the guidance of his advisor, Dr. Selim M. Shahriar, in the conception and writing of this text and the execution of the experiment described herein, as well as for general tutelage in the fields of quantum mechanics and quantum optics. The author would also like to acknowledge the assistance and support of Dr. Gour S. Pati in understanding and conducting the experiment and providing the dayto-day assistance and friship necessary for success in the academic environment. The author thanks Dr. Prem Kumar and Dr. Mary R. Phillips for their supervisory role in the development of this thesis. Finally, the author would like to thank his wife Modhumeta and his daughter Liliana for their love, support, encouragement, and sustaining presence during all of his work. xiii

14 Chapter 1: Introduction 1.1 Overview Optical Raman transitions in neutral atoms have many interesting quantum mechanical properties. Such transitions are useful for carrying out experiments in nonlinear optics, atomic and molecular optics, and quantum computing, among others. The theory of such atom-matter interactions is mature [1]. While this theory is widely believed to be correct, and experiments thus far have validated the theoretical models, continued experimental verification is necessary to determine the accuracy of those models. Experimentation is also needed to demonstrate the potential applications of these effects, to discover the real-world obstacles to realization of theoretically predicted systems, and to determine the limitations of operation of such systems Properties of Rubidium Neutral rubidium atoms in a vacuum environment are particularly well-suited for the study of Raman transitions. Individual atoms in a vacuum environment are analytically simple systems, with few interactions to take into account. Rubidium is plentiful, now believed to be the 16th most common element in the Earth s crust [2]. Neutral rubidium atoms are not significantly affected by stray electric fields in the laboratory environment, as ions would be. The energy level structure of rubidium atoms 1

15 2 ls itself favorably to the study of Raman transitions using near-infrared light, allowing the use of highly accurate optical methods. Naturally occurring rubidium consists of two isotopes: 85 Rb, occurring with 72% abundance, and 87 Rb, occurring with 28% abundance [3]. 85 Rb is stable, while 87 Rb exhibits β decay with a half-life of years. Rubidium has one valence electron; it is the second-most alkaline, second-most electronegative element, after sodium. Similar to sodium, neutral rubidium is explosive when exposed to water (including ambient moisture), rapidly forming rubidium dioxide (or rubidium superoxide) and releasing hydrogen; the hydrogen is ignited by the intense heat of the reaction. Rubidium must be kept under vacuum, and extreme care must be exercised when a cell containing rubidium is emptied or loaded. 85 Rb has a nuclear spin of 5/2, and 87 Rb has a nuclear spin of 3/2 [2] Energy Level Transitions Every atom can exist in one of several energy levels. The possible energy levels are determined by the internal structure of the atom. The primary origin of this structure is the motion of the electrons around the nucleus, as well as the interactions between the electrons and the nucleus and any interactions between the atom and external forces. The actual energy level of the atom is mainly due to the kinetic energy of the electrons, although several other important factors come into play. Put succinctly, the state of the atom determines its energy level. More precisely, each state in which the atom is permitted by its internal structure to exist is called an allowed state, and its corresponding energy level is called an allowed level. Other states and levels are disallowed, meaning

16 3 that it is not physically possible for the atom to exist in such a state (or at such an energy level). This important fact bears repeating: The atom may only exist in one of several discrete states, each with a well-defined energy level. When an atom s electrons are moving in such a way that their combined energy could be no lower, the atom is said to be in the ground state. If the energy level of the atom is higher than the ground state energy, the atom is in an excited state. Some of the atom s allowed energy levels are not precisely the lowest-energy state but are very close to it; these states are also considered ground states. An atom can move from one state to another by absorbing or emitting a photon. The photon s energy must match the difference in energy levels between the two atomic states. The change from one energy level to another is called a transition, or an allowed transition. (Under certain circumstances, even if two energy levels are allowed, the transition between them can be disallowed.) The photon energy is defined by its frequency (or wavelength) via the equation E = h ω = hc λ. E is the energy of the photon, ω = 2π f is the radial frequency of the photon, c is the speed of light in a vacuum, λ is the photon wavelength (also in a vacuum), h is Planck s constant, and h = h 2π. The process of absorbing and emitting photons is generally called scattering, because photons can be re-emitted in different directions (and at different frequencies) than they have when they arrive at the atom. Consider an atom with a ground state and an excited state, and a difference E between the energy levels of the two states; assume the ground-to-excited state transition is allowed. When the atom is in the ground state and a photon approaches the atom, if the

17 4 energy of the photon matches the transition energy E, the atom will absorb the photon and move into the higher energy excited state. This process is unsurprisingly called absorption. If the atom is initially in the excited state when the photon approaches, the photon causes the atom to emit a second, identical-wavelength photon, and the atom returns to the ground state. This process is called stimulated emission. The incident photon and emitted photon typically travel in the same direction, namely, the direction the incident photon followed before it reached the atom. If the atom is left undisturbed in an excited state for sufficiently long, then it will randomly decay into a lower-energy state, emitting a photon of the appropriate wavelength in a random direction. This process is called spontaneous emission; the average time the atom remains in the excited state before decaying is called the excited state lifetime. The process of atomic energy decay is related to a process called decoherence, and the excited state lifetime is related to the decoherence time of the atom. When the energy of the incoming photon matches the transition energy, the photon is said to be resonant with the transition. If the frequency (or wavelength) of the photon is very nearly but not exactly equal to the required frequency, the photon is said to be detuned by a small frequency δ. Detuned photons can still cause transitions, but they 1 do so with a probability reduced roughly by the factor δ ; these are usually called nonresonant transitions, in contrast with the resonant transitions, where δ = 0. If the detuning δ is extremely large, the atom is transparent to the photon; in other words, the photon travels past the atom, and the atom and the photon do not interact.

18 5 When a resonant or detuned laser field is incident on an atom, many photons of the same frequency are impinging on the atom. An atom will go through repeated cycles: first, it absorbs a photon and moves to the excited state; next, stimulated emission causes it to emit a photon and return to the ground state. These cycles are called Rabi oscillations. The oscillation rate is lower for detuned fields than for resonant fields; one can think of this as a result of the lowered probability that an atom is excited by a detuned field Three-Level Systems Figure 1 shows a typical energy level diagram for an atom with three levels. (For the present discussion, an atom will suffice as a three-level system. It should be noted that many other systems function quantum mechanically in the same manner.) Two of the states, a and b, are ground states, with nearly equal energies. The upper level, c, is the excited state. Using the Dirac notation prevalent in quantum mechanics, these states are written as a, b, and c The diagram is not to scale; typically, the energy between the ground and excited states is to times as large as the ground-state separation. We presume that the transitions from a to c and from b to c are allowed. We also assume that the a to b transition is disallowed. Although b is technically a higher-energy state than a, the energy level difference is so small and the lifetime of b so great that an atom in state b will essentially never decay into state a. Transitions may be disallowed for other reasons, but in this example, the reason is simple convenience and scope of consideration. A three-level system is one such as this where only three energy levels are considered. A lambda system, or Λ-

19 6 system, is a three-level system consisting of two ground states and one excited state, with the two ground state-excited state transitions allowed and the ground state-ground state transition disallowed. (It is called a Λ-system because the two allowed transitions resemble the shape of the Greek capital letter lambda.) An atom can be moved from state a to state b by way of state c as follows: An atom in state a is excited to state c by absorbing a photon from a laser tuned to the angular frequency Eac h. A second laser is also incident on the atom with frequency Ebc h. Once the atom reaches state c, it is de-excited to state b by the second laser, and it emits a photon with frequency Ebc h. Such a transition from one level to another by way of a third is called a Raman transition. Note that the atom absorbed one photon at frequency Eac h and emitted one photon at frequency Ebc h ; in effect, one photon was converted from the higher to the lower frequency. This process is called photon conversion or photon frequency conversion. In a collection of many atoms, such as an atomic vapor, many atoms will cause photon conversion, and a fraction of the first laser power will be converted into the second laser frequency. This conversion is known as the Raman effect. The Raman effect has many uses in atomic and molecular optics, both for studying fundamental properties of physics and for building interesting devices. An experiment allowing the stimulation and observation of the Raman effect forms the basis for many current experiments in atomic and molecular optics Rubidium D Line Transitions The absorption spectrum of naturally occurring rubidium is shown in Figure 2. This experiment is primarily concerned with the D2 transitions of 85 Rb, occurring

20 7 between the 5 2 S 1/2 and 5 2 P 3/2 energy levels. These transitions are excited by absorbing (or emitting) photons of 780 nm wavelength. The hyperfine interaction causes splitting of the 5 2 S 1/2 ground state. For this experiment, the F = 2 and F = 3 hyperfine sublevels are used, with a ground-state splitting of GHz. The 5 2 P 3/2 level has four hyperfine sublevels, all spaced within approximately 1 GHz; however, due to Doppler broadening of the vapor cell medium (discussed later), these four sublevels may be treated as a single level. Thus, the two hyperfine 5 2 S 1/2 ground states and the 5 2 P 3/2 excited state form a Λ-system, with the F = 2 to F = 3 transition disallowed, as shown in Figure 3. One other transition sees extensive use in this experiment, and that is the D2 F = 2 transition of 87 Rb between the 5 2 S 1/2 and 5 2 P 1/2 levels. This transition is also at 780 nm; in terms of frequency, it is approximately 1.22 GHz downshifted from the 85 Rb D2 F = 3 transition. Typically, the experiment employs optical beams that are reddetuned (downshifted) from the 85 Rb D2 F = 3 transition by 1.1 GHz; the 87 Rb D2 F = 2 transition readily absorbs these beams, since the detuning from that transition is only 120 MHz [4]. Figure 4 shows a total picture of the relevant energy levels and transitions. 1.2 The Raman Effect In 1928, C. V. Raman discovered that a sample of material scattering light from an intense, monochromatic source can produce scattered wavelengths other than that of the source. This effect is called the Raman effect in his honor, and such scattering is called Raman scattering. The Raman effect has since been studied in great detail. Two

21 8 variations of this effect exist: the spontaneous Raman effect and the stimulated Raman effect Stokes Generation To understand the operation of the Raman effect, consider the Λ-system shown in Figure 5(a). Assume an atom is in state a and is part of a large ensemble of identical atoms (say, a gas sample). Further, assume a laser field, called the pump field (or simply pump), is incident on the ensemble. The pump field has frequency ω1 = ωac δ, detuned from the a c transition by some amount δ. If the atom and an incoming photon interact, then the atom will t not to transition to state c but instead move into state b, emitting a photon at frequency ω2 = ωbc δ = ω1 ωab that is detuned from the b c transition by the same amount δ. The intermediate energy level that is detuned by δ from b is called a virtual level. Although we say that the atom may not strictly exist at that energy level, it behaves in some ways as though it does. In particular, photon absorption and emission happen as if the atom existed at the virtual level for a brief time. The net effects of this process are that the input photon at the frequency ω 1 is converted to an output photon at the frequency ω2 = ω1 ωab and the atom is moved from state a to state b. Since the output photon frequency ω2 = ω1 ωab is lower than the input frequency, the output photon is called a Stokes photon, and ω 2 is called the Stokes frequency. In an ensemble of many atoms, with a pump field of sufficient intensity and proper frequency, enough atoms will demonstrate this effect that the Stokes field will be noticeable.

22 Anti-Stokes Generation If the atom is initially in state b when the photon approaches, then Figure 5(b) applies. The photon will absorb a pump photon at frequency ω 1, transition to state a via the virtual level, and emit a photon at frequency ω3 = ω1 + ωab. Since the emitted photon is at a higher frequency than the input photon, the output photon is called an anti- Stokes photon, and ω 3 is called the anti-stokes frequency. The question of whether a given atom generates Stokes or anti-stokes light then deps on the energy level of the atom at the time of photon arrival. If a material sample could be cooled to absolute zero, all atoms would exist in their lowest-energy ground states. However, at temperatures above absolute zero (such as room temperature), a material sample at thermodynamic equilibrium has atoms in a distribution among available energy levels. In the case of the atom represented by the three-level system in Figure 5, this means that a sample of these atoms at room temperature has some atoms in state a and some in state b. The number of atoms in b is smaller than the number in a by the Boltzmann factor exp( h ω ab kt ), where k is the Boltzmann constant. At room temperature, then, an incident pump at frequency ω 1 would produce both Stokes and anti-stokes radiation The Stimulated Raman Effect As with spontaneous and stimulated emission, the Raman effect has both spontaneous and stimulated varieties. With a single laser incident upon the sample at frequency ω 1, the Stokes and anti-stokes photons are emitted in random directions, and the process is very inefficient. If, say, an additional laser at frequency ω 2, called the probe, is shined on the sample (at the same point as the first laser), the Stokes conversion

23 process becomes very efficient, and the Stokes photons are emitted in the same direction as the laser at frequency ω 2. A similar effect happens for anti-stokes generation if the probe laser is instead at frequency ω 3. (However, the anti-stokes generation process is less efficient than Stokes generation, for reasons discussed in [5].) Because of this strong directionality, the stimulated Raman effect is often called the forward-scattered Raman process. The intensity of the probe field is greater at the output of the sample (due to the Raman effect) than at the input to the sample; this increase in the intensity of the probe field is called Raman gain. Raman gain has been studied extensively in both theory and experiment [6 9] Optical Pumping When only Stokes generation or only anti-stokes generation is desired, another efficiency question arises: A sample at room temperature will exhibit both Stokes and anti-stokes conversion, even under spontaneous Raman emission. How can one ensure that little or no energy is converted from the pump field into the anti-stokes field? The answer lies in controlling the fraction of atoms of the sample in the states a and b (called the population of states a and b ). This is done through a technique known as optical pumping. Consider an intense CW beam (or a very long pulse) tuned to frequency ω bc and incident on the sample. After a long period of time, what will happen to the atoms in the sample? Those in state b will be unaffected by the field. Those in state a will transition from a to c. From state c, most atoms will be stimulated back down to a again, and the process will repeat itself. However, a small fraction of atoms will

24 11 decay spontaneously into state b, where they will no longer be affected by the incident field. Eventually, all of the atoms in the sample will be pumped into state b by the optical field, and the population of state a will be zero hence the name optical pumping. (Throughout this text, optical pump will always be used to refer to the optical pumping beam. Where clarification is necessary, Raman pump will be used to refer to the pump beam used in the Raman excitation process.) Optical pumping can be used when only a Stokes transition or only an anti-stokes transition is desired. 1.3 Applications of Raman Transitions Quantum Memory A quantum computer, if such is to be fabricated, would naturally require some sort of memory device for storing information; this device is usually referred to as a quantum memory. As quantum computers rely on the quantum mechanical property of entanglement to carry information and to perform their functions, it is necessary for this quantum memory to be able to store entanglement. For example, it is widely believed that a quantum computer would use photons for data transmission and atoms for data storage. A quantum memory in this scheme would take a pair of entangled photons and store them by using them to entangle two atoms in a memory cell. Later, these two atoms could be stimulated to reproduce the original, entangled photons. Such a device would be useful not only for quantum computing but also for studying the properties of entanglement. Several schemes for implementing a quantum memory have been

25 12 presented in the literature [10]; the one presented here is believed to be the simplest and most straightforward. A diagram of such a quantum memory is shown in Figure 6. An energy level diagram showing the operation of the quantum memory is shown in Figure 7. A small glass cell containing neutral rubidium vapor acts as the quantum memory. A source of entangled photons, as well as a series of control pulses from a laser, represents the quantum computer attempting to store quantum information in the quantum memory and retrieve the information later. The atoms in the vapor cell act as three-level systems, having states a, b, and c. The atoms in the vapor cell have already been moved into state b using optical pumping. The entangled photon (one of the entangled pair of photons) arrives at the same time as the storage pulse, or write pulse, from the control laser. The entangled photon causes a transition from b to c. The entangled photon is now stored, entanglement properties and all. However, c is an excited state and is not stable; after some time, it will decay to a lower-energy state. The storage pulse causes a transition from c to a, putting the atom in a stable state. Because of the laws of quantum mechanics, the atom is still in an entangled state, meaning the quantum information from the original photon is still stored in the atom. Later, when the computer wishes to retrieve the photon stored in the memory, the control laser ss a retrieval pulse, or read pulse, into the vapor cell. The atom storing the photon sees the pulse, is excited from a to c, and decays down to b, emitting the original, entangled photon. When the read pulse arrives, other atoms in the vapor cell are in state b, meaning they are transparent to the read pulse; in this way, a single photon can be stored in a large

26 13 ensemble of atoms. (In the actual experiment, the transitions excited are detuned from c.) Quantum Entanglement Generation The same process used to fashion a quantum memory out of rubidium vapor can also be used to create a source of entangled photons [11]. When an atom completes a b c a Raman transition, it absorbs a photon of energy energy E bc and emits a photon of E ac. When it completes the reverse transition, it absorbs a photon of energy and emits a photon of energy E ac E bc. The photons emitted by the two Raman transitions are entangled. Thus, the rubidium vapor cell, when stimulated this way, can act as a source of entangled photons for other experiments, such as testing the quantum memory described above Other Experiments Many other experiments are based on the Raman effect and Raman transitions in neutral vapor media. For example, electromagnetically induced transparency (EIT) is a process whereby Raman transitions are excited in a medium such that the medium becomes transparent to a narrow range of frequencies. Just as in the quantum memory device, where optically pumped atoms in the b state are transparent to light at the frequency Eac h, EIT produces a medium which, while under laser stimulation, allows light of a certain narrow frequency to pass through transparently [12]. An EIT medium is also useful for so-called slow light experiments. In such scenarios, the propagation of a single frequency of light through the medium is

27 14 dramatically slowed or even halted. Such an effect may be used to store a laser pulse. Under different conditions, a medium may be placed in such a state that it demonstrates fast light. Fast light, as one would expect, is the propagation of light over a narrow range of frequencies at speeds greater than the speed of light in a vacuum. (Interestingly, it has been shown that even in a fast light medium, information cannot be transmitted faster than the speed of light.) Communication within and between quantum computers also poses an interesting problem that could potentially be solved using the systems described in this text. Quantum information, in the form of entanglement, must be communicated using the principles of teleportation. Detuned Raman transitions in three-level systems offer a promising avenue for the implementation of real-world teleportation [13]. Some progress has already been reported in this area [14 15]. Strong magnetic fields affect the internal structure of an atom. The Zeeman effect causes an atom s energy levels to shift (and even to split) in the presence of a magnetic field. Because of this energy level shift, the frequencies of photons absorbed and emitted by the affected atom change slightly. If this frequency shift is measured very precisely, then a medium exhibiting the Raman effect can be used as a magnetometer. All of these experiments are of great interest at present in the optics community. Although the underlying theory is mature, the effects are not completely understood, and much attention is given to their investigation and comprehension. Once the effects are fully understood, many exciting and novel applications will be developed [16]. All of these effects, however, require an experimental system for testing and observing the

28 15 Raman effect in a medium. The experimental system discussed in this text, while primarily motivated by the quantum memory application discussed above, forms an excellent platform for investigating all of the effects mentioned here.

29 c 16 E ac =hω ac E bc =hω bc b a Figure 1. A three-level system.

30 Transmission Rb 87 F=2 Rb 85 F=2 0.2 Rb 85 F= frequency (GHz) Figure 2. Rubidium absorption spectrum.

31 18 δ =1.1GHz Figure 3. Rubidium levels involved in D2 transitions.

32 19 4 5P 3/2 (F') Pump Optical Pump Pump Probe ~1.22 GHz F = 2 5S 1/2 (F) GHz 6.8 GHz Rb 85 Rb 87 F =1 Figure 4. Relevant energy levels for the present experiment.

33 20 δ c δ c Pump ( ω1) Stokes ( ω2) b Anti-Stokes ( ω3) Pump ( ω1) b a a Figure 5. Raman transitions.

34 21 Pulsed Source of Entangled Photon Pairs Optical Delay Line PBS Coincidence Monitor SP Quantum Memory RP Readout Pulse (RP) Storage Pulse (SP) Figure 6. A quantum memory experiment.

35 Storage: 22 Pump Probe B 1 A 0 Retrieval: Pump Probe A 0 B 1 Figure 7. Energy level structure for a quantum memory experiment.

36 Chapter 2: Experiment Description 2.1 Realization of a Raman System Rubidium atoms in some form are needed to observe Raman transitions. As mentioned in the Introduction chapter, sealed glass cells containing neutral rubidium under vacuum are commercially available. It is also possible to create a closed vacuum system from heat pipes, a vacuum pump, and several grams of solid rubidium. A diagram of the heat pipe cell is shown in Figure 8. Both the glass cell and the heat pipe cell are heated to vaporize the rubidium; increasing the temperature of the cell causes an increase in rubidium vapor density. In vapor form, the rubidium atoms are sufficiently distant from each other to behave essentially as isolated atoms. Thus, neutral rubidium vapor cells provide a convenient method for manipulating isolated rubidium atoms. Lasers generate the photons absorbed by the rubidium atoms during energy level transitions. While lasers produce essentially a single frequency of light, observation of the desired frequencies may require several different frequencies of light. The polarization of the laser light plays an important role in the experiment, so beam splitters, wave plates, and polarizing filters are used to adjust the polarization of the beam. Lenses are used to increase laser intensity where needed. To provide multiple laser frequencies, a portion of the laser beam is diverted through an acousto-optic modulator (AOM), which shifts the frequency of the beam and can pulse the beam, if desired. 23

37 24 Acousto-optic modulators (AOMs) are used to achieve pulsing and frequency shifting. An AOM operated in CW mode consists of a laser input, a radio-frequency (RF) sinusoidal input, and a diffracted, frequency-shifted laser output (see Figure 9). The output laser frequency is shifted by an integer multiple of the frequency of the RF input; different integer frequency multiples, as well as red- or blue-shifting, may be chosen by using different spatial mode outputs from the AOM. A separate microwave frequency counter indicates the exact frequency of the AOM RF sinusoidal input. Because the entry and exit apertures of the AOM are so small, a focusing lens must be placed before the AOM input, and a collimating lens must be placed at the AOM output. The output from the laser is used to generate the optical pumping, write, and read pulses. To achieve pulsed-mode operation, a RF switch is connected to the RF input of each AOM. The RF switch pulses the beam by switching the RF input on and off based on a TTL control pulse. The RF switch acts in essence like a mixer, gating the sinusoid on when the TTL pulse is high and switching the sinusoid off when the TTL pulse is low. If CW-mode operation is desired instead of pulsed operation, the RF switch may be driven by a TTL high level. The combination of AOMs and polarization-changing optical components, along with the appropriate control circuitry for the AOMs, can produce any desired combination of laser pulses or continuous-wave (CW) laser beams. With these tools, the rubidium atoms in the vapor cell may be manipulated in any fashion. In order to verify the behavior of the rubidium atoms and the effects of the incident light, a system is needed to detect and characterize photons emitted by the rubidium atoms. The detection

38 25 system consists primarily of a single-photon-counting avalanche photodiode (APD), along with an advanced array of detection electronics. A scanning Fabry-Pérot spectrum analyzer provides spectral characterization of the output signals. A standard photodiode for detecting higher-intensity signals is also available as part of the detection system. A polarization- and frequency-selective filtering and absorption scheme protects the sensitive detection electronics and blocks undesired signals. Polarization filtering is performed using the same kinds of polarizing optics as in the generation of the incoming light signals. Absorption filtering using the 87 Rb D2 transition is carried out using additional rubidium vapor cells, as discussed in the Energy Level Transitions subsection. Although the signals to be absorbed are not precisely tuned to the 87 Rb D2 transition, the absorbing vapor is Doppler-broadened and absorbs signals over approximately a 1 GHz band. The atoms in the rubidium vapor have a net kinetic energy and are moving in random directions relative to each other and relative to the observer. Because of this motion, the atoms each see a slightly different Doppler-shifted light frequency. As a result, the absorbing rubidium vapor s energy levels are effectively broadened from narrow lines into ranges on the order of 1 GHz wide Phases of the Experiment The experiment history can be delineated into roughly three different phases, each motivated by a slightly different goal. The three phases moved sequentially, each phase building successively on the progress and maturity of the prior phase. Phase I focused on the observation and characterization of Raman gain in the vapor medium under CW illumination. Phase II saw the evolution and refinement of experimental details to

39 increase accuracy and flexibility in the experimental setup. Phase III changed to a pulsed excitation regime and new vapor cells. The results from Phases I and II are applicable to both a fast-light gyroscope and a quantum memory, as discussed in the Applications of Raman Transitions section, while Phase III is devoted specifically to developing a quantum memory or quantum entanglement source. Figure 10 summarizes the three experimental phases. 2.2 Phase I Raman Gain The first objective was to demonstrate Raman gain in the vapor cell medium. Figure 11 shows an overview of the experiment. Two detuned CW beams, the pump beam and the probe beam, illuminated a heat pipe vapor cell to excite the 85 Rb D2 F = 2 and F = 3 transitions, as shown in Figure 12. The probe beam stimulated the F = 3 transition with a detuning of 1.1 GHz. The pump beam operated on the F = 2 transition and was far detuned from the transition; the pump detuning was 1.1 GHz plus the ground state splitting of GHz, or about 4.1 GHz total. Both beams were red-detuned, i.e., downshifted. Because the pump and probe detuning matched the ground state splitting, the Raman effect could be observed between the two ground states. The goal was to see gain in the probe beam; the pump, acting on the 87 Rb D2 F = 2 transition, was absorbed in a second heat-pipe vapor cell Initial Setup The primary laser was tuned to the pump frequency, and the probe beam was generated by passing a portion of the pump beam through a pair of AOMs each tuned to

40 GHz, or half the ground state splitting. The pump was horizontally polarized, and the probe was vertically polarized; a polarizing beamsplitter recombined the two beams before they entered the Raman vapor cell. Later in the experiment, a horizontally polarized, counter-propagating optical pump beam from a second laser, tuned to the 85 Rb D2 F = 3 transition, entered the Raman cell through another polarizing beamsplitter. The third optical window on the heat pipe cell offered a view of the infrared fluorescence inside the cell, which could be seen with an infrared viewer to verify proper operation of the cell. A transverse optical pumping configuration was also attempted but was ineffective, largely due to the geometry of the vapor cell and the difficulty of supplying enough optical pump power to the active region inside the vapor cell. Polarizing beamsplitters filtered out the Raman pump and optical pump beams to a high degree and allowed the probe beam to pass through to the detector. The heat-pipe absorption cell also absorbed both pump beams, allowing the probe to pass. (The majority of the optical pump beam power was absorbed in the Raman cell, and the polarization filtering and the absorption cell filtered out any leakage or scattering.) Later in Phase I, the absorption cell was rearranged into a double-pass configuration to improve absorption characteristics. Initially, a photodetector connected to an oscilloscope formed the detection system. The oscilloscope showed the amount of light incident on the detector. The experiment was run once with only the Raman pump shining on the medium (i.e., with the probe beam blocked), in order to determine the amount of background radiation incident on the detector after filtering and absorption. The experiment was run a second

41 28 time with only the probe shining on the medium, to determine the amount of light in the probe beam itself. Finally, the experiment was run once with both beams both beams illuminating the vapor cell. Raman gain was verified by observing that the light level with both beams active was higher than the sum of the individual detection levels; in other words, with both beams on, some of the pump power was converted into light at the probe frequency. The remainder of the pump was absorbed and not seen by the detector The Fabry-Pérot Spectrum Analyzer As a second step, a scanning Fabry-Pérot cavity was added immediately before the detector. A Fabry-Pérot cavity, also called a resonator, consists of two mirrors separated by a small space and facing each other along the beam axis. Most light is reflected back from the first mirror; however, the mirror is not perfectly reflecting, and a small amount of light enters the cavity. If the wavelength of that light is an integer multiple of the round-trip distance between the mirrors, the light resonates and is ultimately transmitted through the cavity. In this way, the cavity acts like a narrowband, wavelength-selective filter, where the wavelength passed by the cavity is a function of the distance between the mirrors. In a Fabry-Pérot spectrum analyzer, a piezoelectric crystal attached to one of the mirrors allows that mirror to be translated by an applied voltage. The mirror scans back and forth, and the resonant wavelength of the cavity changes with the mirror position. As the cavity scans across a range of wavelengths, the oscilloscope records a trace of the output from the cavity; this trace shows the spectrum of the light impinging on the cavity.

42 29 Adding the Fabry-Pérot cavity to the detection system allowed the collection of spectral data and made the Raman gain process easier to observe and to measure. The pump and probe frequencies appeared as separate lines on the spectrum. Because of this, the absorption of the pump and the gain in the probe could be measured accurately and indepently. A standard technique used in conjunction with Fabry-Pérot cavities is a locking circuit. Fabry-Pérot cavities are extremely sensitive to vibration, and small changes in the cavity mirror position produce sharp changes in the resonant wavelength of the cavity. A locking circuit actively compensates for vibration by shifting the movable cavity mirror slightly in response to vibrations detected. Locking often requires an extra beam in addition to the locking circuitry. Two techniques, a DC side lock and a dithered lock using a lock-in amplifier, were attempted during Phase I. Both kinds of locks were successful in reducing the effects of vibration on the cavity and in stabilizing the amplitude of the detected signal. The locked Fabry-Pérot cavity operated as a stable, robust frequency-selective filter. However, it was determined that spectral resolution of the signal was far preferable to detection of only a single frequency. Brief trials with a locked Fabry-Pérot cavity revealed that laser intensity fluctuations contributed far more variation to the light level than any vibrations in the Fabry-Pérot cavity. Additionally, it was anticipated that scattering of the high-intensity locking beam would hamper detection of extremely low-light signals. Thus, the idea of locking the Fabry-Pérot cavity was abandoned.

43 2.3 Phase II Experimental Refinements 30 Phase II saw several important refinements to the experiment established in Phase I. Light levels were reduced until the experiment entered the single- and few-photon regime, and a photon-counting system was introduced. The existing heat pipe Raman cell was swapped for a glass vapor cell. The glass vapor cell was characterized and proved to have both sufficient performance and highly desirable experimental characteristics, and so a glass Raman vapor cell was used for the remainder of the experiment. Finally, magnetic shielding was introduced to reduce the stray magnetic fields picked up by the Raman cell Single Photon Detection The first step in Phase II involved the use of lower light levels, which in turn required a more sensitive detection system. A single-photon counting module replaced the photodetector. The single-photon counting module is based on an avalanche photodiode (APD), and it emits a short pulse every time a photon is detected. To ensure accurate operation of the APD, the incident light was restricted to less than one million incoming photons per second, or a light level of approximately 0.25 pw. The APD emits discrete pulses, rather than a continuous voltage level, so the APD output was connected to a dedicated photon counting device and to a scaler. The photon counter displays a single number, namely, the number of photons counted in a second. The scaler counts the number of photons detected over series of short, consecutive, equal-duration time windows (or time bins) and then displays a graph of the photon count in each time bin. Both devices require accurate, synchronized trigger signals, and both devices may be

44 31 operated under computer control or indepently. The scaler also offers the option to record data traces. Data recorded from the photodetector-oscilloscope system and the APD-scaler system were plotted and analyzed on a computer. The use of a computer offered a great deal of analytical flexibility as well as the capacity to store an essentially unlimited amount of historical data. Both features proved useful throughout the experiment. Thus, Phase II established a detection system that could record single-photon or classicalintensity data with highly accurate time and spectral resolution and unlimited flexibility in analysis. At low light levels, the APD detected additional spectral lines that were not visible in Phase I. While the probe line was still the strongest, several lines were seen above and below the probe line. Extensive analysis and verification showed these lines to be Stokes and anti-stokes converted photons from both 85 Rb and 87 Rb. These lines provide interesting effects that hinder some applications and help others Glass Raman Cell Although the heat pipe cell provided a high-density vapor, heat pipe cells have several features that make them experimentally difficult to handle. The cell must be continually vacuum-pumped and water-cooled. It is large and unwieldy. Heating the large, thick metal cell walls to vaporize the solid rubidium requires a lot of heat, and hence a lot of electrical current; the cell heating coils were attached to a variable transformer connected directly to line voltage. Line voltage itself provides a 60 Hz AC magnetic field, which induces the Zeeman effect in the rubidium atoms, shifting the line

45 32 spectra slightly. Rubidium vapor is emitted from one arm of the cross-shaped heat pipe cell into the center of the cross, so the rubidium atoms have a net velocity; this net velocity ts to increase the Doppler broadening of the pump and probe lines. While Doppler broadening is usually desirable for the absorption spectrum, sharp spectral lines are important in the Raman cell. Even in the absorption cell, an excessively high degree of Doppler broadening can be too much of a good thing. Finally, the heat pipe cell must be reloaded with solid rubidium samples from time to time, as the vaporized rubidium is eventually removed from the system by the vacuum pump. Solid, neutral rubidium is extremely explosive and requires extreme care in handling, as discussed earlier. A commercially available glass vapor cell solves many of these problems. The glass cell is sealed, requiring no vacuum pump. The cell is cylindrical, approximately 2.5 cm in diameter and 6 to 8 cm long, making it much smaller than the heat pipe cell. The cell is made of Pyrex glass, allowing it to be heated to sufficiently high temperatures to increase the vapor density and vapor pressure, but the smaller cell requires less heat and no cooling. Fiberglass-insulated heating wire is wrapped around the cell to form heating coils; these heating coils can be connected to a DC power source, rather than to stepped line voltage, since they require much less current. Glass vapor cells are commercially available and do not need to be fabricated in the laboratory. A glass cell will eventually lose its vapor and must be replaced; however, the cost of a single glass cell is often much less than the cost of a single sample of solid rubidium to be loaded into the heat pipe cell, and the glass cell lasts much longer. The glass cell has optical-quality windows at either, causing no beam distortion. Although the optical windows may

46 33 be coated with an anti-reflective coating, an uncoated glass cell was used for the experiment, introducing a slight reflection of approximately 4%. (The glass cell windows have a slight wedge angle to prevent further back reflections.) The glass cell was originally supposed to have a vapor density too low to allow observation of the desired effects. However, at this point in the experiment, the heat pipe cell was replaced with the glass cell, and the Raman gain in the glass cell was observed. It was found that, while the Raman gain was lower in the glass cell due to a lower vapor density, the gain was sufficiently high to proceed with the experiment. (The additional Stokes and anti-stokes lines in both 85 Rb and 87 Rb were also present at power levels roughly similar to those seen in the heat pipe cell.) The glass Raman cell thus permanently replaced the heat pipe Raman cell in the experiment. One aspect of the experiment made more difficult by the particular choice of glass cell was optical pumping. Cross-propagating optical pumping was found to be effective, as with the heat pipe cell. However, transverse optical pumping was made virtually impossible by the cylindrical shape of the glass cell. Although cross-shaped glass cells with four optical-quality windows are available commercially, the glass cell used in the experiment at the time was cylindrical and had only two optical windows. A cylindrical lens was used to focus the transverse optical pumping beam into a short line (as opposed to a small circular spot, as with a typical spherical lens). Unfortunately, the side of the glass cell, while appearing smooth to the eye, was not optically smooth and caused too much deflection and distortion of the beam for transverse optical pumping to be effective.

47 Magnetic Shielding The Zeeman effect had been observed in the heat pipe cell at times and was also present in the glass cell, mainly due to the magnetic field induced by the current in the heating coils. The allowed energy levels of an atom are primarily dictated by protonelectron interactions. The energy levels are resolved first in terms of the energy of the electron s orbit around the nucleus. Fine splitting of the energy levels is caused by the electron spin (which induces a small magnetic field) interacting with the electron orbit. Hyperfine splitting is accounted for by considering the tiny magnetic field due to nuclear spin in addition to electron orbit and electron spin. An external magnetic field applied to the atom will naturally cause further energy level splitting. This splitting due to an external magnetic field is called the Zeeman effect. The Zeeman effect is a nuisance in this experiment, as it broadens (and ultimately splits) the pump and probe spectral lines. Even if the Zeeman effect were desired, the experimentalist would want control over the magnitude and direction of the magnetic field, probably using external magnetic coils. The heating coils of the cell must carry a particular current to heat the cell to the proper temperature, and so the user may not use the heating coils to vary the induced magnetic field. While Zeeman splitting was less noticeable with the lower current used to heat the glass cell than with the high current used with the heat pipe cell, the effect was still present to a small degree in the glass cell. Additionally, stray magnetic fields (from sources other than the heating coils) can induce Zeeman splitting in the rubidium vapor, although this proved not to be an issue in the current experiment.

48 35 The first, and probably most important, step taken to reduce Zeeman splitting was the bifilar winding of the heating coils. A diagram of the winding and wrapping of the heating coils is shown in Figure 13. The heating coil was bent in half and twisted, much like a twisted pair of communications wires. The magnetic field induced by the DC current in the coil would then be concentrated between the two twisted conductors and not outside the twisted coil. The twisted coil was then wrapped in a spiral fashion around the cylindrical cell. With the heating coil so wrapped, the magnetic field inside the cell due to the heating coil was found to be immeasurably small, even for large heating currents. The second step taken to reduce Zeeman splitting was the construction of magnetic shielding. The shielding was constructed out of thin sheets of magnetic shielding metal, and its shape can best be described as a cylinder fit snugly inside a box. The box is rectangular with square s, and holes are drilled in the shielding at several points for cell mounting and to allow forward and transverse beam propagation. Two anti-helmholtz magnetic coils are also mounted inside the shielding to allow application of a controlled magnetic field, although this feature has not been used thus far. The shielding was found to be effective, and the field inside the shielding was immeasurably small, even when the Earth s magnetic field could be measured outside the shielding. However, because the magnetic shielding is heavy and relatively unwieldy, and because the laboratory environment is essentially free of strong magnetic fields, the magnetic shielding is typically not used. Stray magnetic fields in the laboratory and the Earth s magnetic field have little or no observable effect on the vapor cell medium.

49 2.4 Phase III Pulsed Excitation 36 Whereas Phases I and II used CW lasers to excite rubidium transitions, Phase III moved to a pulsed excitation scheme. This phase of the experiment focused on the applications of quantum memory and quantum entanglement generation using 85 Rb. To avoid the additional 87 Rb spectral lines, which are a source of loss for this application, an isotopically pure glass vapor cell containing only 85 Rb vapor was obtained. After the 85 Rb Raman cell was put in place, the beam paths and AOMs were reconfigured to allow pulsing of the beams entering the vapor cell. The pulses launched into the Raman cell are a long optical pumping pulse and shorter write and read pulses. Optical pumping from the second laser was done away with. When the heat pipe absorption cell was found to absorb over too broad a frequency range, it was replaced with a glass absorption cell (incidentally, the same glass cell that served as the Raman cell in Phase II). Finally, the focus of the experiment has recently moved from spectral characterization to photon correlation and photon number correlation, wherein the entangled nature of Ramangenerated photons may be demonstrated [17] Isotopically Pure Raman Cell For the applications specific to Phase III, the additional spectral lines due to 87 Rb interfere with the operation of the system and are considered a source of loss. For this reason, a cross-shaped glass vapor cell containing isotopically pure 85 Rb was obtained. The cell geometry resembles two cylinders that intersect at their midpoints, one 8 cm long, one 5 cm long, and both approximately 2 cm in diameter. Each of the four arms s in an optical-quality window, thus allowing for transverse optical pumping. Heating

50 37 coils were wrapped bifilarly around the cell as with the mixed-isotope cell. Once the 85 Rb cell replaced the mixed-isotope glass cell as the Raman cell, the 87 Rb lines disappeared, thus verifying the Phase II analysis of the origins of the spectral lines Pulsed Excitation Using AOMs Figure 15(a) shows a diagram of the energy levels that ideally would be used in pulsed excitation of the vapor medium. The optical pumping pulse is still tuned to the 85 Rb D2 F = 3 transition, pumping atoms into the F = 2 ground state; however, it now co-propagates with the other beams, rather than being counter- or transverse-propagating. The optical pumping pulse duration is on the order of 1 ms. When a photon is present in the F = 2 mode, a far-detuned write pulse causes Raman transitions from F = 2 to F = 3 and absorption of the F = 2 photon. A resonant or slightly detuned read pulse excites a Raman transition from F = 3 back to F = 2, and the atom re-emits the stored photon in the process. The read pulse should be highly efficient and cause the read transition with high probability. Both the write and the read pulse last approximately 1 µ s. The delay from the optical pumping pulse to the write pulse is on the order of 1 µ s, and the write-to-read delay is around 200 ns. All of the pulses must occur within the optical pumping decoherence time, i.e., before the atoms optically pumped into the F = 2 state experience decoherence and return to the F = 3 state. Figure 14 shows a pulse timing diagram. (Decoherence in a vapor cell is largely due to collisions of atoms and energy exchanges in collisions.) Certain experimental difficulties make the level scheme pictured in Figure 15(a) impractical. Most notably, the excitation pulses must be absorbed and not reach the

51 38 detector, while the Stokes and anti-stokes signal photons must pass through. One solution to this problem is shown in Figure 15(b). The optical pump is resonant and is completely absorbed by 85 Rb. The write pulse is detuned from the F = 2 transition by 4.1 GHz, the same amount as the Raman pump detuning in Phases I and II. The write pulse is thus completely absorbed by 87 Rb, while the Stokes photon is passed through the absorption cell. The write pulse is also used as a read pulse; although it is detuned from the F = 3 transition, it is still efficient enough to cause the read transition. The anti- Stokes photon is then detuned from the F = 2 transition by a sufficient amount not to be absorbed. One drawback to this approach is that the read pulse, which causes a F = 3 to F = 2 transition in atoms already pumped to the F = 3 state, will also cause a F = 2 to F = 3 transition (i.e., a write transition) in atoms remaining in the F = 2 ground state. This difficulty may be avoided by reducing the pulse powers, as discussed later, so that only one atom is excited per pulse. A second option, shown in Figure 15(c), was also considered. In this case, the optical pump frequency is used for the read pulse. Unfortunately, in this case, the anti-stokes photon is absorbed by the 85 Rb F = 2 transition, as it is resonant at that frequency. Initially, the pulse powers were high enough that several atoms make the appropriate write and read transitions. However, the collective excitation mode necessary for entanglement of vapor cells as macroscopic ensembles (discussed briefly in the Theory chapter) requires that exactly one atom in the entire vapor be excited from the F = 3 to the F = 2 state. Once the write and read transitions have been verified, the

52 pulse powers will be reduced until only, on average, less than one Stokes or anti-stokes photon was detected after each pulse Glass Absorption Cell As the read transition used in Phase III is nearly resonant, it falls within the 87 Rb absorption spectrum in the highly Doppler-broadened heat pipe absorption cell. A heat pipe cell was chosen as the absorption cell for the same reasons that a heat pipe cell was originally chosen as the Raman cell, and it has all of the same advantages and drawbacks. However, since the read signal was being absorbed, it was determined that a glass cell would be used as the absorption cell. The glass cell used for absorption was the mixedisotope cell originally used in Phase II as the Raman cell. Once heated sufficiently, the glass cell proved to be as effective as the heat pipe cell in absorbing the optical pump and write pulses. The glass cell s absorption lines were broad enough for proper absorption of the excitation pulses but narrow enough to allow the signal to pass. Originally, the heat pipe cell was left in the beam path and simply not heated, meaning no vapor was present in the cell and the cell had virtually no effect on the beam. Once the glass vapor cell proved more useful, the heat pipe cell was removed from the beam path entirely Photon Correlation and Photon Number Correlation For the Raman vapor cell to work correctly as a quantum memory or quantum entanglement source, the Stokes and anti-stokes photons emitted during the write and read pulses must be entangled. Entanglement is best demonstrated using a photon correlation measurement, also called a start-stop experiment. The experiment works as

53 40 follows: In the single-atom excitation regime, when the write pulse is active, the singlephoton detector waits for a photon detection event. When the event occurs, an external device begins counting the time until a second photon is detected. Under ideal circumstances, the second photon detected will be the anti-stokes photon generated by the read pulse. However, photon emission is a random process; additionally, detector noise and stray light may cause either the first or second detection event. To establish the entanglement of the two photons, the experiment is run many times, and the distribution of inter-photon arrival times is plotted. A strong peak in the distribution should occur near the time between the write and read pulses, indicating that the majority of photons are the Stokes-anti-Stokes pairs desired. An additional experiment, called a number correlation experiment, is used when the pulses are operated at a higher light level. In this case, many photons are generated during each write and each read pulse. The majority of the photons detected, though, should be the Stokes-anti-Stokes pairs desired, and so the number of photons detected during the write pulse should be strongly correlated to the number of photons detected during the read pulse. This experiment is performed by counting the number of photons detected during the write pulse, separately counting the number of photons detected during the read pulse, and then comparing the two numbers. However, in this case, the read pulse may also generate write transitions, as discussed before, so the verification process is somewhat more complicated. Because the photon correlation and number correlation experiments perform statistical measurements, they must be run for thousands or millions of repetitions before

54 41 results can be obtained. Computer control of experimental equipment is required for the rapid experiment repetition rates and result aggregation required. Sophisticated pulsing and synchronization are also used. More details about computer control and synchronization are given in the chapter entitled The Detection System. 2.5 Experimental Details The experimental layout consists conceptually of laser frequency generation and tuning, vapor cells, absorption and filtering, and detection (see Figure 16). The experimental details below are organized in that fashion, with the exception that specifics of detection components are covered in The Detection System. Following the experiment details are specific details about each phase of the experiment. A full schematic diagram of the experiment in Phases I and II is shown in Figure 17. A diagram of the Phase III experiment is shown in Figure Laser Frequency Generation and Tuning The main laser is an optically pumped Coherent 899 titanium-doped sapphire (Ti:Sapphire) ring laser tuned to output approximately 700 mw in continuous-wave (CW) mode at a wavelength of nm (verified by a Burleigh wavelength meter). The Ti:Sapphire laser output is linearly polarized, has a linewidth of 1 MHz to 5 MHz, and has a spot size of 2 mm. The pump laser is a Coherent Innova 400 water-cooled argon ion CW-mode laser operating in multi-line visible spectrum (MLVS) mode at approximately 12 W output power. The Ti:Sapphire laser can be tuned over a broad frequency range and locked to a specific frequency by way of an attached reference

55 42 cavity. A small part of the laser output is diverted to a saturated absorption setup, a glass rubidium vapor cell and a photodetector, so that the laser frequency can be locked relative to any 85 Rb or 87 Rb D2 transition. Figure 19 shows the typical saturated absorption spectrum. The laser may also be set to scan every 250 ms over a broad frequency range, or an external voltage may control the laser frequency (although this last feature is seldom used in the present experiment). The secondary laser used for optical pumping in Phases I and II is an identical Coherent 899 Ti:Sapphire ring laser pumped by an identical Coherent 400 argon ion laser; all other parameters of the secondary laser are identical to those of the first, and the secondary laser also feeds a small saturated absorption setup of its own. AOMs perform frequency shifting and pulsing. A given AOM is rated for a particular center frequency; diffraction efficiency and output laser power decrease as the AOM is operated at a frequency farther and farther from the rated center frequency. For example, the ground-state splitting in Phase I is provided by two 1.5 GHz AOMs operating at GHz, which results in high diffraction efficiency. If 1.2 GHz AOMs were operated at that frequency instead, the diffraction efficiency would be near zero, resulting in virtually no laser power at the output of the AOM. Brimrose, Intra-Action, Crystal Technology, and Isomet manufacture AOMs of the type used in the experiment; available AOMs have center frequencies of 1.2 and 1.5 GHz, as well as 90, 200, and 270 MHz. Electronics are also needed to provide the RF signal needed to drive the AOM. Typically, an AOM driver is used, which provides a tunable frequency source and an appropriate power level for the AOM. In some cases, an AOM driver is fashioned from a

56 43 DC voltage source, a voltage-controlled oscillator (VCO), and an amplifier with an appropriate bandwidth. In either case, the AOM driver is connected to the AOM through a RF switch, which allows the AOM to be pulsed on and off. Figure 20 shows the relative shift of the pump and probe beams using a cell absorption trace, indicating that the AOMs are properly configured Vapor Cells The vapor cell used in Phase I is a custom-made, vacuum-pumped heat pipe rubidium vapor cell. The heat pipe cell is configured in a cross shape, with optical quality windows on three arms and a heat pipe oven making up the fourth arm. The heat pipe oven resembles a half-open section of pipe. The oven contains a 5 g ampoule of neutral rubidium in its natural isotopic distribution, i.e., 72% 85 Rb and 28% 87 Rb. The oven has a nozzle at the connection point with the rest of the cell. The input and output light pass through the windows on the two arms adjacent to the oven. The third window, opposite the oven, allows for observation of fluorescence inside the cell, which indicates proper absorption. Heating coil (as in the case of the glass Raman vapor cell) is wrapped tightly around the entire oven and attached to a variable transformer (variac) supplied by 120 VAC line voltage. The oven nozzle section has a separate heating coil with its own variac, and a third heating coil and variac heat the pipe sections closest to the three windows. Chilled water runs through copper tubing soldered to the cell midsection. During operation, the windows and nozzle are heated highest, and the oven is heated only slightly, to preclude rubidium condensation on (and clogging of) the optical windows and oven nozzle. Typical temperatures are 420 K or less for the window sections, 420 K for

57 the nozzle, and 370 K for the oven. Higher temperatures are required when the rubidium ampoule is nearly depleted. Vacuum pumping maintains the cell vacuum around 0.01 torr (around 1.33 Pa); vapor densities as high as approximately atoms cm can be achieved. For Raman operation, the center of the cell is located at the focal point between two lenses of 2.5 cm diameter with focal lengths 400 mm and 200 mm, respectively. The cell is held in place by a series of circular clamps attached to optical mounts. Two glass vapor cells are used in the experiment, a mixed-isotope cell and an isotopically pure 85 Rb cell. The mixed-isotope cell is a sealed glass cylindrical cell containing rubidium vapor under low vacuum, with optical-quality windows at either of the cell. The mixed-isotope vapor consists of a naturally-occurring distribution of rubidium isotopes, i.e., 72% 85 Rb and 28% 87 Rb. The cell is cylindrical, 10 cm in length and 2.5 cm in diameter, with optical-quality windows at either. The windows have a small wedge angle to prevent direct back-reflections of incoming laser beams. In the 85 Rb cell, the cell vapor is greater than 90% isotopically pure. The cell is cross-shaped; its geometry is that of a 8 cm long cylinder intersected at its midpoint by a 5 cm long cylinder, creating a cross-shaped container. Both cylinders are 2 cm in diameter and in optical-quality windows with small wedge angles. The shorter arms allow the use transverse optical pumping beams. The vapor density can be as high as approximately atoms cm. For Raman operation, light is focused at the center of the glass cell, as with the heat pipe cell. Each cell is glued to an optical mount and either mounted directly on the optical table or placed inside a magnetic shielding box.

58 45 To increase the density of rubidium vapor within each glass cell, a heating coil is wound around the cell and attached to a 0 A to 3 A DC current source. The coil consists of nickel-chrome wire inside a braided fiberglass insulation sleeve of 2 mm diameter (rated to house 16 AWG wire). The heating coil is wound bifilarly, as shown in Figure 21. A length of coil is cut and bent in half. The b point is twisted until the entire length of wire becomes like a twisted pair cable. The twisted coil is then wound in solenoid fashion around the glass cell and tied in place at the s of the cell using copper wire. Some glass is left exposed near the center of the length of the cell to allow the transverse optical pumping beam to enter the cell. It is important to note that rubidium inside the vapor cell will t to condense where the cell is coldest. As such, it is important to wind the coils tightly near the window sections to reduce or prevent rubidium condensation on the optical windows. (If any rubidium condenses on the windows, proper heating can vaporize and remove the condensed metal.) During operation, the cell is heated to a temperature of approximately 320 K by a DC current of approximately 1.0 A. The glass vapor cells can be mounted inside a somewhat complicated magnetic shielding box, shown in Figure 22. The box itself is 16.5 cm long with 11 cm square removable caps; the box is made of two layers of 0.5 mm thick magnetic shielding foil, and the caps are made of three layers of 0.2 mm thick magnetic shielding foil. The box fits snugly around a five-layer open-ed cylinder of 0.2 mm thick magnetic shielding foil. The cylinder, in turn, fits snugly around a pair of identical anti-helmholtz coils, located at the s of the cylinders. The anti-helmholtz coils consist of 50 turns of

59 46 20 AWG enamel-coated copper wire wound around a light wooden former. The coils allow for active cancellation or induction of magnetic fields, but the coils are not currently used. Holes are drilled in the caps to allow light to pass in and out of the cell; a similar hole is drilled in the side of the box (and cylinder) to allow the transverse optical pumping beam to enter the cell. A small hole is drilled in one cap for the mounting post. Tiny holes are drilled in the caps for the leads from the anti- Helmholtz coils. A Gaussmeter was used to measure the magnetic field inside the cell. A magnetic testing cell was fashioned out of an open-ed roll of paperboard of the same dimensions as the glass cell; the paper cell was mounted on a similar optical mount and wrapped in a second, identical heating coil. A hole was cut in the side of the paper cell to allow the Gaussmeter probe to enter through the transverse optical pumping hole in the shielding and measure the magnetic field in the center of the cell. After calibrating the Gaussmeter and applying current to the heating coil, the magnetic field reads as less than 35 mg, or below the noise margin of the Gaussmeter Absorption and Filtering In order to shield the detection setup from the strong laser pulses used in the experiment, both polarization and frequency filtering are used. The photons of interest are the photons emitted during the pump and probe transitions. Any other photons not absorbed during the pump or probe transitions are considered noise and must be filtered out before they reach the detector. Noise photons include optical pump, Raman pump,

60 and probe photons not absorbed by the Raman medium, as well as any photons scattered by the medium or by the experimental optics. Polarizing beamsplitter cubes provide the majority of the polarization filtering. The optical pump and write pulse are horizontally polarized, and the read pulse is vertically polarized. A 1 cm polarizing beamsplitter cube with an extinction ratio measured at 30 db acted as the primary polarizing filter, located just after the Raman vapor cell (see Figure 23). Polarizing beamsplitters exhibit polarization mixing, whereby a small component of horizontally-polarized light is mixed with the vertically-polarized output and vice versa. Due to polarization mixing, the use of additional polarizing beamsplitters will not increase the extinction ratio. After the absorption vapor cell (discussed below), a polarizing filter is used to further ensure single polarization. Because of the choice of energy levels, 87 Rb is used as a frequency-selective absorbing medium. The off-resonant D2 F = 3 transition in 85 Rb closely matches the D2 F = 2 transition in 87 Rb, making 87 Rb an excellent absorber of the write pulse and any scattered light from the optical pumping beam. A heat pipe rubidium vapor cell is used in a double-pass configuration as the primary absorber. The absorption heat pipe cell is identical to the Raman heat pipe cell. The double-pass configuration ss the beam through the cell twice, using slightly different locations in the cell each time (so that the same vapor atoms are not excited by the first and second passes). At the output of the vapor cell, the beam polarization is rotated 90 by a half-wave plate; a polarizing beamsplitter after the wave plate separates the second pass beam from the first, and another before the cell input allows the first and second passes to be combined. Typical 47

61 48 temperatures for the cell heating are identical to those of the Raman heat pipe cell, i.e., 420 K or less for the window sections, 420 K for the nozzle, and 370 K for the oven. Under these conditions, absorption of the optical pumping and write beams is more than 70 db Phase I, II, and III Details Figure 24 shows the frequency spectrum used in Phase I. The laser frequency is locked to the Raman pump frequency, or 1.1 GHz below the 85 Rb F = 3 transition; the optical pump laser is locked to the 85 Rb F = 3 transition. The probe beam is generated from the Raman pump beam by pair of 1.5 GHz AOMs, each operating at a frequency of GHz, or half of GHz. The AOMs operate in CW mode, i.e., the radio frequency (RF) sinusoidal input to the AOM is not switched on and off. The Raman pump and optical pump are horizontally polarized, and the probe is vertically polarized. Since the goal of Phases I and II was to observe Raman gain in the probe, this choice of polarizations allowed the use of polarization filtering. In Phase I, the Raman and absorption vapor cells were both heat pipe cells with a shared vacuum pump and chilled water connections. In Phase II, the mixed-isotope glass vapor cell replaced the heat pipe Raman vapor cell. The heat pipe absorption cell remained in place. The frequency scheme used was the same as that of Phase I (see Figure 24). In Phase III, the spectrum used was slightly different than that of Phases I and II. The Phase III spectrum is shown in Figure 25. Additionally, the signals were pulsed by sing appropriate TTL pulses to AOM RF switches. A 200 MHz AOM is used to

62 49 pulse the optical pump. The laser is red-detuned from the 85 Rb F = 3 transition by 200 MHz; when the optical pump is pulsed on, the AOM blue-shifts the optical pump back up to resonance with the F = 3 transition. The write and read pulses are generated from the laser by a 1.2 GHz AOM operating at 1.0 GHz. As a result, the write and read pulses are red-detuned from the F = 3 transition by 1.2 GHz, putting them at nearly the same frequency as the Raman pump in Phases I and II. The AOM switching pulses come from the pulse generation setup described in greater detail in The Detection System. The optical pumping pulse and the write/read pulse are vertically polarized. The 85 Rb vapor cell became the new Raman cell, the mixed-isotope glass cell became the new absorption cell, and the heat pipe absorption cell was removed. (During this time, the mixed-isotope cell came unglued from its mount. Since this cell no longer needed to be mounted inside the magnetic shielding box, it was not re-glued; rather, it was mounted using two circular clamps on optical mounts. Several layers of aluminum foil were wrapped around the heating coil to protect it from the circular clamps.) Other Modifications Although the experiment can be broken down roughly into three phases, some small side experiments were carried out to accomplish specific objectives. The most noteworthy of these is the measurement of the absorption spectrum of the various vapor cells, such as in Figure 26. For this experiment, the laser control was set to scan over a frequency range of 5 to 10 GHz, the Fabry-Pérot cavity was removed from the beam path, and the photodetector trace was averaged over many scans and recorded on the oscilloscope. Only one beam and no AOMs were used.

63 50 An additional experiment that was carried out was a heterodyne detection experiment, using specialized high-frequency photodetectors. Any photodetector detects the intensity (and envelope) of the incident light. In a heterodyne setup, two beams are superimposed. The field incident on the photodetector then consists of more than one frequency component (due to the multiplicity of beams). When the detector measures the incident intensity, this is equivalent to taking the magnitude squared of the field strength (to within a scaling factor). If the photodetector output is viewed on a spectrum analyzer, peaks will appear at the sum and difference frequencies of the input beams (called the beat note of the heterodyne signal). This is useful because the strength of those peaks deps on the input power of both input beams, and thus one strong input beam may be used to amplify another, weaker beam through heterodyne detection. Additionally, this technique allows for accurate resolution of the individual frequency components of a signal.

64 Figure 8. Heat pipe cell diagram. 51

65 52 Input beam Input beam Sinusoid Input beam AOM AOM RF switch AOM Output beam (order 1) TTL gate signal Pulsed output (a) (b) (c) Figure 9. Acousto-optic modulator (AOM) schematic.

66 53 Phase I Phase II Phase III Objective Characterize Single-photon Photon correlation vapor medium spectral resolution and entanglement Mode CW CW Pulsed Raman cell Heat pipe Glass 85/87 Glass 85 Absorption cell Heat pipe Heat pipe Glass 85/87 Detection Photodiode Photon counting Photon counting Spectral resolution Yes Yes No Figure 10. Summary of the three experiment phases.

67 54 PBS λ/2 Laser 1 Laser 2 λ/2 Pump Probe AOM 1 AOM 2 Optical pump PBS Raman Rb cell PBS Absorption Rb cell PBS Probe λ/2 Attenuators APD Fabry-Perot cavity Polarizing filter PBS Photodetector Figure 11. Phase I and II experiment diagram.

68 55 4 5P 3/2 (F') Pump Optical Pump Pump Probe ~1.22 GHz F = 2 5S 1/2 (F) GHz 6.8 GHz Rb 85 Rb 87 F =1 Figure 12. Relevant energy levels for the present experiment.

69 Figure 13. Heating coil wrapping. 56

70 Figure 14. Pulse timing diagram. 57

71 F=4 58 F=1 δ =1.2 GHz Optical pump Read F=2 (a) Write F= GHz F=4 F=1 F=4 F=1 δ =1.2 GHz OP Write, read OP, read Write F=3 F=3 (b) (c) Figure 15. Energy level structure for pulsed excitation.

72 Figure 16. Block diagram of experiment. 59

73 60 PBS λ/2 Laser 1 Laser 2 λ/2 Pump Probe AOM 1 AOM 2 Optical pump PBS Raman Rb cell PBS Absorption Rb cell PBS Probe λ/2 Attenuators APD Fabry-Perot cavity Polarizing filter PBS Photodetector Figure 17. Schematic diagram of Phase I and Phase II of the experiment.

74 61 PBS λ/2 Laser 1 PBS λ/2 AOM 1 AOM 2 OP Read Raman Rb cell Absorption Rb cell Write 50/50 BS λ/2 Probe APD PBS Attenuators Polarizing filter Figure 18. Schematic diagram of Phase III of the experiment.

75 Transmission Rb 87 F=2 Rb 85 F=2 0.2 Rb 85 F= frequency (GHz) Figure 19. Saturated absorption spectrum for rubidium.

76 Raman pump magnitude Probe time Figure 20. Relative shift between pump and probe.

77 Figure 21. Heating coil wrapping. 64

78 shielding box transverse optical pumping hole 65 Rb cell mount cylindrical shield anti-helmholtz coils Figure 22. Magnetic shielding for glass vapor cells.

79 66 λ/2 Probe Figure 23. Location of polarizing beamsplitter cube performing primary polarization filtering.

80 Raman pump Optical pump GHz Transmission Probe 87 Rb F = Rb F = 3 δ 1.1 GHz Frequency (GHz) Figure 24. Frequency spectrum used in Phase I and Phase II.

81 Write beam Optical pump Transmission Rb F = 2 Laser Rb F = 3 δ 1.2 GHz Frequency (GHz) Figure 25. Frequency spectrum used in Phase III.

82 New cell 6 5 Normal cell 4 3 Saturated absorption Figure 26. Typical absorption spectrum measurement.

83 Chapter 3: The Detection System 3.1 Overview In order to verify that the desired effects actually occur in the experiment, the experimental detection system needs to be a highly accurate, flexible system capable of taking multiple kinds of measurements. The ability to plot, manipulate, and store the data on a computer is vital. The detection system must be synchronized to the rest of the experiment, particularly when operating the experiment in the pulsed excitation regime. Finally, the detection system must be reasonably simple to operate, so that extensive training is not needed and few things can go wrong during data collection. Several kinds of measurements must be made. Both classical light levels on the order of 10 µ W to 100 mw and low light levels on the order of 1 to photons/sec must be observed. Often, spectral resolution is desirable; sometimes, inter-photon arrival times are important. Virtually all data must be recorded over time, and these traces must be manipulated, analyzed, and saved for future reference. In particular, the computer software package MATLAB, published by The MathWorks, is used for all plotting and analysis; all data must up in MATLAB in some form. MATLAB revision 13 (version 6.5) was used for this experiment; at present, MATLAB revision 14 (version 7) is available and is likely to provide similar results. Although MATLAB runs on several platforms, the computer used for data analysis in this experiment is an IBM-compatible PC running Windows 2000 and connected to the 70

84 71 university network. (It is inted that the computer be upgraded to Windows XP in the future. No obstacles to this upgrade are foreseen.) The detection system consists of a Fabry-Pérot cavity-based spectrum analyzer, a series of neutral-density filter wheels (attenuator wheels), a classical photodetector, and an avalanche photodiode (APD) operated in single-photon counting mode. Figure 27 shows a diagram. The detection system has features for meeting all of these needs, as well as providing the flexibility needed to adapt to the changing needs of the experiment. The system can be reconfigured quickly if a new kind of measurement is desired to track a previously unseen event. The data recorded can be transferred to computer in a straightforward manner. Custom MATLAB software, as well as a program developed in the LabVIEW environment from National Instruments, was written to handle data transfer and to aid analysis of the data. With modern technology and modern laboratory equipment, a great deal of complexity and automation is made possible. However, the development, refining, and verification of complex systems take time, and system faults are made ever more likely with increasing complexity. Many times, a decision must be made as to the worthiness of developing a particular component or a particular feature of the system; often, the decision is whether to integrate and automate a set of operations that otherwise would be performed manually. For the present experiment, the general rule was that a particular component is worth developing if the development, testing, and use of a system will require less time over the life of the experiment than manually performing the same tasks. This rule was not always followed, especially in cases of error-prone or non-existent

85 72 manual procedures or high-cost automation components. It is believed that the resulting system makes optimal use of available technology to enable and speed experiment progress without excessive cost. A discussion of the detection system is perhaps best pursued in a task-oriented manner. The description that follows is arranged in order of specific tasks, each roughly corresponding to a phase of the experiment. (See The Detection System for more information on Phases I, II, and III of the experiment.) This ordering also follows the chronological development of the experiment and the detection system. More background information about the theory and operation of Fabry-Pérot cavities is contained in Appix A: Fabry-Pérot Cavities. LabVIEW software documentation can be found in Appix B: LabVIEW Documentation. MATLAB source code can be found in Appix C: MATLAB Source Code. 3.2 Spectral Resolution of a Classical Signal One important task is the recording of a spectrally resolved, classical-level signal. This was an integral capability in Phase I of the experiment (see Experiment Description). The measurement is carried out by scanning the Fabry-Pérot cavity, measuring the cavity output with a classical photodetector, and recording the trace on an oscilloscope. Attenuator wheels allow the detection of excessively strong signals without sacrificing detector performance.

86 The Fabry-Pérot Spectrum Analyzer The Fabry-Pérot cavity consists of two circular mirrors 2.5 cm in diameter. One mirror is fixed, and one mirror is movable. The movable mirror is mounted on a piezoelectric crystal. With an applied voltage, the crystal deflects by V/nm and is linear over a range greater than 0 V to 250 V. Typically, the cavity mirrors are spaced approximately 1 cm apart, giving a free spectral range (FSR) of 174 V, or a halfwavelength at 780 nm; the FSR may also be expressed as 14.9 GHz. The cavity FSR may be changed by dismounting and re-mounting the fixed mirror. At resonance, the cavity transmits approximately 70% of the signal power and has a finesse of about 45 with a line width of about 260 MHz. The cavity was custom-made of aluminum and has three hand screws for alignment. The Fabry-Pérot cavity may be removed from the beam path and reinserted with relative ease. The Fabry-Pérot piezoelectric crystal is driven by a triangle wave signal coming through a high-voltage amplifier from a function generator. The high-voltage amplifier is custom-made. The function generator is a Stanford Research Systems DS MHz function and arbitrary waveform generator. (At times when the DS345 is unavailable, a BK Precision model 4011A 5 MHz function generator is used instead; however, the DS345 is preferred.) The function generator produces a 10 Hz triangle wave with a 2.3 V amplitude and a 0.12 V offset. The function generator also puts out a synchronization pulse to indicate the start of the positive and negative half-cycles of the triangle wave. Because of the DC signal offset, the rising edge of the sync pulse comes approximately one sixth of a cycle before the triangle wave goes from falling to rising, and the falling

87 74 edge of the sync pulse occurs a half-cycle later. The high-voltage amplifier is an inverting 500 V amplifier that clips negative voltages. The amplifier output is monitored on a two-channel oscilloscope through a probe that attenuates by a factor of 10. The high-voltage amplifier output begins to distort the triangle wave at frequencies between 10 Hz and 100 Hz. At 10 Hz, RMS distortion of the triangle wave is less than 0.6% (see Figure 28) Neutral-Density Filter Wheels The attenuator wheels are standard neutral-density filter wheels, available from any optics supply company. Each filter comes with front and back wheels, and each wheel may be moved indepently to select an attenuation level. The attenuation levels are measured in optical density (OD), where 1 OD = 10 db. One wheel can be turned to a value of 0.04, 0.1, 0.2, 0.3, 0.4, or 0.5 OD, and the other wheel can select filters of 0.04, 0.5, 1.0, 1.5, 2.0, or 2.5 OD, giving a total range of 0.08 to 3.0 OD, roughly in steps of 0.1 OD. The attenuator wheels cause little or no beam distortion. One wheel is placed before the Fabry-Pérot cavity, and two wheels are placed before the input to the APD The Classical Photodetector The classical photodetector is located after the output of the Fabry-Pérot cavity. A flip mirror diverts the beam path from the APD input to the photodetector. The photodetector is a Thorlabs model PDA55 photodetector with a ± 12 V DC power supply, and it is capable of detecting envelope fluctuations in the light up to 10 MHz. The photodetector has an effective area of 2 13 mm. The gain in the photodetector can be

88 75 selected as 0 db to 40 db in steps of 10 db, with a roughly constant gain-bandwidth product. The photodetector clips near 10 mw input light power at 0 db gain. The output of the photodetector is connected to an oscilloscope. When the Fabry-Pérot cavity is used, the oscilloscope displays a spectral resolution of the light signal. As the Fabry- Pérot mirror scans over a free spectral range, the oscilloscope shows both the scan voltage and the cavity output, giving the frequency spectrum of the light signal The TDS 3012 Digital Oscilloscope The oscilloscope is a Tektronix TDS 3012 portable, two-channel digital oscilloscope. It has a 100 MHz analog bandwidth, a maximum signal input of ± 10 V, a sampling rate of up to 1.25 GS/s, and indepent 9-bit input channel digitization. It includes the same basic features of all modern oscilloscopes, as well as some additional mathematical and triggering functions. It can be triggered by a threshold crossing on one of the two input channels or by an indepent triggering signal. It can run continuously or acquire and display a single trace. It has both RS-232 and GPIB control interfaces. Additionally, it can read traces from and write traces to a MS-DOS-formatted 1.44 MB floppy disk. It is this last feature which enables the transfer of data to a computer Computer Interfaces The oscilloscope can write data files in several formats, The most universally accessible is comma-separated value (CSV) format, a format often used for spreadsheets. In this format, the time and voltage values of the oscilloscope trace are saved as two rows in a matrix, i.e., one time point and one voltage per line. This format has the advantage

89 76 of being extremely easy to import into MATLAB (via the csvread command), as well as being a human-readable text format. However, a typical TDS3000-series data trace contains data points, each of which has one time and one voltage coordinate. As a result, the CSV files produced by the oscilloscope are roughly 170 kb, and only eight such files fit on a standard 1.44 MB floppy disk. Additionally, since floppy drives are rather slow, it takes over 60 s to save traces of both oscilloscope channels in this format. The oscilloscope also allows traces to be saved in the oscilloscope s internal format, with a filename extension of.isf. (Usually, the filenames follow the pattern tek00000.isf, with incrementing numbers for each file saved on a single floppy disk.) In this format, the oscilloscope stores the data in binary form, making the file size an average of only 20 kb. The format is native to the oscilloscope, meaning no conversion is required to write the file. These two factors make file internal-format files quicker to save than CSV files by a factor of three. Additionally, the internal file format contains the major settings of the oscilloscope at the time the data trace was taken, making internal-format files more informative than CSV files. Tektronix publishes the details of the internal file format. A MATLAB command, read_tds3000, was written to read the internal-format files copied to the PC. The command is robust and correctly parses any file that adheres to the specification published by Tektronix. The TDS 3012 oscilloscope has both RS-232 serial and GPIB control interfaces. It would therefore be possible to transfer data traces from the oscilloscope to the PC using either a serial or a GPIB connection; such a connection would also allow automated operation of the oscilloscope, if such were desired. However, such an interface takes

90 77 time to develop, and the existing method of saving data to a floppy disk is sufficiently quick and simple for the purposes of the present experiment Performance The performance of this system was sufficient for Phase I of the experiment. The Fabry-Pérot cavity is able to resolve spectral lines separated by approximately 0.25 GHz. For continuous wave (CW) excitation at a classical light level, the photodetector resolution was more than adequate. Intensity fluctuations in the laser and noise in the high-voltage amplifier make the light level fluctuate by more than 3%, and sometimes by as much as 10%; such fluctuations are difficult to overcome, and 3% accuracy is sufficient for measurements in Phase I. As stated, it takes roughly 20 s to save two data traces to the floppy disk. Typically, the Fabry-Pérot triangle wave and the photodetector output are saved to disk simultaneously. While the system in its present form is not able to take measurements at a high repetition rate, Phase I does not require rapidly-repeated identical measurements, such as for statistical measurements. As such, the classical spectral-resolution detection system performance is ample. 3.3 Spectral Resolution at Low Light Levels At low light levels (i.e., single-photon or low-photon-count levels), the photoncounting avalanche photodiode (APD) replaces the classical photodetector. Although this is essentially the only change to the detection system optics, the photon-counting nature of the APD requires much more complicated support electronics, and the detection

91 78 system becomes more complex. The optical connection to the APD is also more complicated than simply shining the beam on the detector The Photon-Counting APD The APD is a Perkin-Elmer SPCM-AQR-16-FC with a dark count of 25 counts/s. It is extremely sensitive to stray light and is housed inside a dark protective box (see Figure 29). The box is fashioned from a double layer of black, paper-covered foam boards approximately 5 mm thick. (The foam boards are of the kind used for presentations and poster displays.) The box dimensions are approximately 53 cm wide by 26.5 cm deep by 26.5 cm tall. Edges and corners are taped with black electrical tape, and the base of the box has a black felt skirt approximately 7.5 cm wide to cover areas where cables enter and leave the box. The APD has a fiber connector, a power supply, a signal output, and a gate input. The gate input can be used to switch the APD on and off. Multi-mode optical fiber connected to a fiber coupling lens is used to bring light in from the beam to the APD. Typically, as much as 90% of the light power is coupled into the fiber. The coupling lens is mounted on an optical mount and is protected by a 2.5 cmdiameter barrel approximately 22 cm long. The barrel contains a narrowband filter that filters out all but the range 755 nm to 805 nm, with approximately 50% transmission over that range. At 17 cm away from the coupling lens, the barrel tapers to 1.25 cm in diameter. A small iris is placed near the open of the barrel; the iris aperture is approximately 4 mm in diameter. Two filter wheels are placed between the iris and the Fabry-Pérot cavity. A shroud fashioned from three black foam boards and a long piece of black felt cover the coupling lens, the barrel, the iris, and one filter wheel. The part of the

92 79 optical fiber outside of the APD box is spiral-wrapped in two to three layers of black electrical tape; otherwise, light entering the fiber through the cladding increases the APD dark count. Black foam board walls shield the APD box and coupler shroud from the rest of the experiment and also are placed at key points throughout the optical table to reduce reflections. Typical experimental dark counts are on the order of 100 counts/s with the iris blocked by a black foam board. The APD has a quantum efficiency of approximately 58% and is linear up to photons/s. Between photons/s and photons/s, a correction factor must be applied, and above photons/s, the APD saturates. Extreme input illumination can permanently damage the APD. In the present experiment, the APD is never exposed to light levels above photons/s. The APD requires the use of a large heat sink, although this is less critical at light levels below photons/s. The APD requires a 5 V power supply that can supply as much as 2 A. The APD power supply was fashioned out of a computer power supply. Details of the APD power supply are listed in Appix A: APD Power Supply. The APD output pulses are between 1 V and 2 V high into 50 Ω and are approximately 35 ns wide; the pulse has a sharp rising edge and a slow exponential decay. There is a 60 ns dead time between pulses, during which no photons can be detected. This dead time would limit the maximum observable photon flux to photons/s; however, the APD is operated under much lower light conditions. The APD has a probability of 0.5% of after-pulsing, i.e., issuing a second pulse for a single photon.

93 80 Certain kinds of APDs may be used simply as extra-sensitive photodetectors, and their output voltage levels vary with the incident light level. However, because the SPCM-AQR series are photon-counting APDs, their outputs are pulsed, and an oscilloscope is not suitable for recording measurements. The pulses must be counted digitally and typically summed over some time window to evaluate the APD output correctly. The pulse counting is performed by the SR400 and the SR430, discussed below. The APD has a gate input that may be used to disable the APD temporarily. While the gate is off, the APD does not generate any output pulses. However, the gating function is somewhat complicated. Although the APD datasheet claims that a TTL low level will gate the APD off, this is not strictly correct. The gate input drives current when the gate is disabled, and not all TTL sources can sink current while generating a low voltage. In order to connect a TTL pulse to the gate via a 50 Ω cable, a small transistorbased circuit is required. A simplistic example circuit, and the one used in this experiment, is shown in Figure 30. The TTL input is connected to the transistor base, and the collector is connected to the APD gate input. One additional factor complicates the gating process. After the APD gate input is switched high, the APD takes approximately 500 ns to recover. During this time, it emits no pulses. At the of the 500 ns, the APD always emits a single pulse [18]. Shortly after this single pulse, the APD resumes its normal operation.

94 The SR400 Photon Counter The Stanford Research Systems model SR400 Photon Counter is a dual-channel photon counter, inted for counting photon detection pulses from a photon-counting APD or a photomultipler tube (PMT). The pulse detection discriminator threshold is user-settable between 0.3 V and 0.3 V, with either a rising or falling slope. The SR400 trigger and clock may be either externally or internally generated. Total counts can go as high as photons before an overflow occurs. Additional features and more complicated counting modes than the ones described here are available. The basic counting mode of the SR400 involves counting pulses over a specified range of time (called the count window), waiting a certain time (called the dwell time), and optionally repeating the process a fixed number of times or indefinitely. The accumulated count is displayed on the unit s two-line LCD both as it accumulates and after counting has finished. The count window may be as short as 100 ns or as long as ms. The minimum dwell time is 2 ms using internal triggering, or as short as about 1.4 ms when using an external trigger. Both the count window and the dwell time may be specified to one significant figure, e.g., 30 clock cycles or 300 clock cycles but not 310 clock cycles. As an example, the SR400 is typically configured in the present experiment for a count window of 1 s and a dwell time of 0.5 s. The SR400 then counts pulses over a period of one second, displaying the count as it accumulates; when the one-second period is complete, the final count is displayed for a half-second before the count is restarted. In this particular configuration, it is possible to see the number of photons incident on the

95 82 APD per second, allowing a quick estimate of whether the APD is operating in a nonlinear or saturation regime. Typically, the SR400 is left running whenever the APD is powered up, in order to detect quickly any sudden increase in photon flux and protect the APD from damage. The SR400 has a digital-to-analog (D/A) output and generates an analog voltage on that output that varies either linearly or logarithmically with the final count at the of the count window. As the count is completed, the D/A voltage is changed to match the new count; the D/A voltage is not changed again until another count completes. This allows the SR400 count to be displayed graphically on an oscilloscope. However, as the minimum dwell time is 2 ms, the counter resolution becomes extremely limited. A count cycle (a count window plus a dwell time) can not be any shorter than slightly over 2 ms. As the count cycle becomes shorter and shorter, the dwell time becomes a greater and greater fraction of the count cycle time. Since photon arrival and photon counting are statistical processes, they must be averaged over some time or some number of repeated measurements to produce accurate results. For example, a 100 ns count window with a 2 ms dwell time means that the photon counter is only counting for 0.005% of the count cycle. The resolution cannot be increased past 2 ms, and the short count window means that the photon count will have a high variance. Increasing the count window to 1 ms will increase the accuracy of the count, but already the count cycle time has been increased to 3 ms, leading to a loss in resolution. Even a count cycle near 2 ms limits the resolution to 50 data points per 10 Hz Fabry-Pérot cycle. As a result, the SR400 cannot be used with an oscilloscope for data storage.

96 83 The SR400 also has serial and GPIB interfaces, allowing complete control of the instrument by computer. The SR400 can store up to 2000 consecutive counts per channel; these counts can be retrieved via serial or GPIB connection. A serial connection was attempted, and some success was achieved in retrieving count results in this manner. However, the 2 ms dwell time again presented a resolution problem. Additionally, the serial interface proved unreliable, even with RTS/CTS handshaking (also called hardware flow control). It is unknown whether this was due to the SR400, the serial programming features of MATLAB, or both. Reading all 2000 counts off the two-line SR400 display would have been an extremely laborious, manually intensive, error-prone process and, as such, was not attempted. As the SR400 has no other data interface (e.g., floppy disk drive), data collection could not be performed using the SR400. The SR400 served only as a visual count monitor for the experiment The SR430 Scaler/Averager The Stanford Research Systems SR430 Multi-channel Scaler/Averager can be thought of as the graphical equivalent of the SR400. It has a single data input and a trigger input. It records the number of pulses in each of a large number of identical, consecutive time bins, and it plots the resulting counts on a graphical display. The time bins can range from 5 ns to 10 ms in duration, and the total number of bins may be varied from 1024 to in increments of 1024, with no dead time or dwell time between bins. The SR430 can also accumulate the results over repeated runs (from 1 to runs or indefinitely). Additional, slightly more complicated modes of operation, as well as additional features, are available. The SR430 has both RS-232 serial and GPIB interfaces.

97 84 The primary unit of execution of the SR430 is a scan. When the user presses the Start button, the SR430 waits for a trigger. A trigger signal is mandatory. Once the trigger is received, the SR430 begins to count pulses in the first bin. Immediately after the first bin is complete, the SR430 stores the bin count and begins counting pulses for the second bin. Counting continues this way, with no dead time between bins, until the preset number of bins is reached (from 1024 to ). Once this number of bins has been reached, the SR430 has completed one record. The number of records per scan may be set from 1 to If more than one record per scan has been requested, then when one record is complete, the SR430 repeats the process, waiting for a trigger and then adding pulse counts to each bin in order. In this way, the SR430 can accumulate multiple records in a single scan. The SR430 has several important features that are not used in the present experiment. If the number of records per scan is set to zero, the SR430 will accumulate indefinitely, until the user presses the Stop/Reset button. The SR430 has options for subtracting records from the accumulated total instead of adding them. The SR430 can either alternate between adding and subtracting records or may subtract records marked by an external add/subtract TTL signal. There is also an option to delay the start of data acquisition up to time bins after the arrival of the trigger signal. The SR430 can save trace data to a MS-DOS-formatted 720 KB floppy disk for transfer to a PC. The trace data is saved in binary format; Stanford Research has documented the binary file format. The floppy disk is used to transfer data to the PC. A MATLAB command, read_sr430, has been written to read the SR430 trace data files into

98 85 MATLAB. The command returns the relative time offsets of each bin, the bin counts, and optionally the SR430 settings contained in the trace data file. The SR430 floppy drive is only compatible with 720 KB floppy disks. As such disks are difficult to find presently, it is easiest to fashion one out of a 1.44 MB floppy disk by covering the disk density marker hole in the corner of the disk (opposite the write-protect switch) with a piece of tape. Unfortunately, as the disk is used repeatedly to transfer files from the SR430 to the PC, the tape covering the density marker becomes stretched out, and the floppy drive sensor detects the disk as a 1.44 MB disk. This results in data read errors; on the PC, the operating system usually identifies the disk as unformatted at this point. Removing the floppy disk and adjusting or reapplying the tape fixes the error. The SR430 also offers the option of serial and/or GPIB control. GPIB control was attempted later; see the Computer Control of the Detection System section. Serial control proved to be unfruitful. The interface s primary utility is in data transfer from the SR430. However, using the serial port interface, data transfer is forced to occur in text mode, rather than binary mode. Ill-conceived text-mode formatting forces each bin count to be transferred using a zero-padded format that results in an average of 14 bytes transferred per bin; at the maximum serial data rate of bit/s, with one start bit, one stop bit, no parity bits, and 8-bit data words, this results in a transfer time of 120 s. Additionally, the SR430 s serial interface shows similar unreliability to the SR400 s, due to the SR430, MATLAB, or both. When the Fabry-Pérot cavity is used with a 10 Hz triangle wave, the SR430 is configured for a bin width of 5.12 µ s and bins per record. At these settings, and

99 86 with the appropriate trigger timing, the SR430 records the APD output for the entire positive-going half-cycle of the Fabry-Pérot scan as well as some additional buffer time before and after that half-cycle. In this way, the entire signal spectrum is recorded. Furthermore, the user can visually identify the start and of the half-cycle in the data file by virtue of the two mirror-image lines that can be drawn at the boundaries between each half-cycle (see Figure 31). The SR430 manual lists the maximum trigger rate as 2400 Hz; that rate is achievable only using particular settings of the SR430 and not in the general case. In practice, the SR430 is usually triggered at 10 Hz and never faster than 100 Hz, due to limitations in other parts of the detection system. The number of records per scan is usually either one or several hundred, but rarely are more than a thousand records accumulated in a single scan. At a triggering rate of 10 Hz, one thousand records take 100 s to collect. Additionally, saving the trace data to floppy disk takes approximately 30 s. While this amount of time is considerable, it is sufficient for most manual measurements taken during the experiment. The exception to this is the regime of high repetition rate photon correlation and photon number correlation experiments; for those cases, a GPIB control program was developed in LabVIEW. Once the LabVIEW control program was developed, it largely replaced floppy disks for data transfer to the PC, even for low repetition rate experiments. For spectrally resolved measurement experiments, the resolution is determined by the Fabry-Pérot cavity; as such, the low light level detection system offers intensity resolution to the single photon level but no increase in spectral resolution over the classical light level detection system.

100 3.4 Pulsed Excitation and Pulse Control 87 In order to have a pulsed excitation experiment, it is necessary to s enable pulses to the AOM RF switches. These enable pulses must be carefully timed and synchronized. For this purpose, a pulse generator is used. The DS345 function generator has a TTL sync output; this sync signal is used as the master trigger for the rest of the system. The DS345 is set to run at 10 Hz, as before. Since the Fabry-Pérot cavity is not used in pulsed mode (see below), higher triggering rates are possible when the highvoltage amplifier is temporarily disconnected from the function generator ramp output Pulse Generation The pulse generator is a Quantum Composers model 9514 pulse generator, operated in external trigger mode. In this mode, the generator requires a trigger input and generates four TTL pulses of arbitrary duration and delay from the input trigger. The delay and duration settings are accurate to within 10 ns, with less than 400 ps of jitter. Each pulse may be specified as positive, negative (inverted), or disabled. Of the four output channels of the pulse generator, Channel 1 generates the optical pump pulse, Channel 2 generates the write pulse, and Channel 3 generates the read pulse. As described in The Detection System, the optical pumping pulse is about 1 ms long, the write pulse is about 1 µ s long and follows the optical pumping pulse by about 1 µ s, and the read pulse is about 1 µ s long and follows the write pulse by about 200 ns. A timing diagram is shown in Figure 32. Channel 4 of the pulse generator provides the SR430 trigger, and the same signal is also used sometimes to generate an APD gate signal. The SR430 trigger pulse s rising

101 88 edge is placed near the of the optical pumping pulse, as the primary observations are of the effects of the write and read pulses. The SR430 is not sensitive to the pulse duration, so the pulse duration is adjusted to gate the APD appropriately. Typically, the APD gate is enabled from 1 µ s before the of the optical pumping pulse to some time shortly after the read pulse. The AOMs are pulsed on and off by the TTL pulses from the pulse generator. As described in the Experiment Description chapter, the pulsed mode of operation involves the use of either the optical pumping beam or the write beam as the read beam. As such, one beam needs to be pulsed twice. For this purpose, TTL digital logic is used to combine the pulses. A 74LS32 quadruple OR gate is mounted on a small circuit board inside a small enclosure with BNC connectors for power supply, input, and output; two dual-input OR gates are made available through the enclosure. The OR gate is sufficiently fast to combine pulses of the widths involved. (It was discovered that floating inputs cause the OR gate output to float high.) The AOMs switch on and off cleanly and sharply with the pulses supplied. At times during the course of the experiment, particularly when component alignments need to be readjusted, it is convenient to have a CW beam, rather than a pulsed beam. To simulate a CW beam, the pulse generator outputs can be inverted, or the pulse durations can be increased to nearly 100% of the trigger repetition period. In this way, the AOMs are switched on for nearly a 100% duty cycle.

102 Photon Detection For pulsed operation, fine resolution of a short range of data is required. For this purpose, the SR430 is typically set to a bin width of 5 ns and a count of 1024 bins per record. These settings allow the recording of 5.12 µ s of data with 5 ns pulse resolution. Occasionally, the pulses used are wide enough to require a higher bin count. It should be noted that in the case of pulsed excitation, the Fabry-Pérot cavity is not used. The write and read pulses are extremely close together in time, less than 1 µ s apart, and well-separated in frequency, more than 3 GHz shifted. The cavity can not be scanned fast enough between pulses to transmit both frequencies at the appropriate times. One occasional use of the Fabry-Pérot cavity in pulsed mode is as a frequency-selective filter. Ideally, the function generator would generate a DC voltage that would hold the cavity at the appropriate spacing. However, the DS345 function generator does not generate a sync pulse when set to a frequency of 0 Hz. Instead, the function generator is configured to generate an extremely small-amplitude ramp with a DC offset corresponding to the desired DC voltage level. The small-amplitude ramp is buried in the noise at the output of the high-voltage amplifier driving the Fabry-Pérot piezoelectric crystal, so the same effect is achieved. However, the cavity mirror spacing drifts noticeably over the course of a minute, probably due to thermal expansion. If the cavity is left at the same DC voltage, it will typically drift off the transmission peak within 600 s. Photon correlation and photon number correlation experiments require a finer degree of control over data acquisition. To perform those kinds of measurements, one must keep traces from many repetitions of the pulse sequence. While the SR430 can

103 90 accumulate and sum records, it cannot store more than a single record of accumulated data. To save each individual record, computer control is needed; see Computer Control of the Detection System below Performance Typically, the system is operated at the same 10 Hz used to generate the Fabry- Pérot triangle wave, even though the Fabry-Pérot cavity is typically not used for pulsed excitation experiments. A repetition rate of 10 Hz is usually sufficient for present purposes. If the high-voltage amplifier is disconnected from the function generator, the repetition rate can be increased as high as 100 Hz. Operation at repetition rates above 100 Hz is not advisable; the optical pumping pulse is between 1 ms and 3 ms in duration, and the vapor cell population needs time between repetitions to relax after the write and read pulses. Although a large number of records may be accumulated quickly, it is not possible to store a long string of individual records At first glance, the 5 ns bin width of the SR430 would seem to be unnecessarily accurate, given the 60 ns dead time of the APD. However, it should be noted that a bin width of 5 ns allows the accurate resolution of pulse start times. The fact that the APD has a 60 ns dead time should not be taken to mean that the APD pulses indicate photon arrival only to within 60 ns, or that the APD can only emit a pulse during consecutive 60 ns windows, like a digital system with a 60 ns clock period. Rather, the APD pulses may occur at any time, and the 60 ns dead time simply indicates a period after the pulse during which no more pulses may be emitted (see Figure 33).

104 3.5 Computer Control of the Detection System 91 For certain kinds of experiments, it is not sufficient to accumulate records on the SR430. When individual photon count traces from many repetitions are required, computer control of the SR430 is needed. A computer program commands the SR430 to run a single scan; when the scan is completed, the program reads the SR430 s trace data and stores it. The program then repeats the cycle. Each run-finish-read cycle is called an experiment cycle, or simply a cycle. The computer program controls the SR430 using the GPIB interface; data is also transferred via GPIB. The program was developed using the LabVIEW programming system from National Instruments. Version of the LabVIEW Full Development System was used GPIB GPIB, or General Purpose Interface Bus, is a standard interface used to control test and measurement equipment such as the SR430. IEEE standard defines virtually all aspects of the interface, from signal timing to cable requirements. IEEE defines commonly-used additions to the GPIB specification. Aside from a basic set of commands defined by IEEE 488.2, the command set and data structure are not specified by IEEE 488 but are defined by the instrument manufacturer. As a historical note, GPIB was originally developed at Hewlett-Packard and was then called HP-IB; older Hewlett-Packard equipment still carries the HP-IB label on compatible ports. HP-IB was adopted as an IEEE standard in 1973 and renamed GPIB.

105 92 The data collection PC has a National Instruments PCI-GPIB host card residing in an available PCI slot. This card, along with appropriate driver software from National Instruments, allows the PC to act as a controller for GPIB devices. A GPIB-compliant cable connects the PC to the SR430. If desired, the PC could control multiple devices using the same GPIB connection by chaining cables from the PC (or the SR430) to the other devices. Commands are sent to a GPIB-compliant device in ASCII (text) format, and responses are also returned from the device in ASCII format. Usually, one command is sent per transaction. This format is also common for RS-232 instrument control interfaces; in that case, one command is issued (or one response is returned) per line. Devices that have both GPIB and RS-232 interfaces typically support nearly identical command sets on both interfaces. However, devices often support binary data transfer only over GPIB; GPIB uses 8 bits per byte transferred, while RS-232 supports 7 or 8 bits per byte (and, in uncommon variations, as few as 4 bits per byte). The SR430 is IEEE compliant. Its GPIB interface operates at a raw data rate of approximately 250 kbit/s, much lower than the IEEE maximum of 8 Mbit/s. The SR430 will only transfer binary trace data over GPIB. In binary format, each bin count is represented by a two-byte number in little ian order (i.e.,.least significant byte first). At this rate, the SR430 requires approximately 70 ms to transfer 1024 bins of data or approximately 1 s to transfer bins of data. This offers a drastic improvement over the 120 s required for a complete data transfer over RS-232. It is

106 93 important to note that binary transfer over GPIB requires the entire trace to be transferred at once. All bins in a record are transferred. Once the driver software is installed on the PC, the control program can be written in any of a variety of languages, including C/C++. However, LabVIEW is often used for GPIB instrument control and has a rich set of features for GPIB communication. Many simplified, instrument-specific interfaces have been developed for LabVIEW to allow easy implementation of control programs while avoiding some of the more complex details of GPIB communication. LabVIEW was chosen as the development system based on its extensive GPIB support and based on the expertise of laboratory staff LabVIEW The LabVIEW development environment is a graphical environment. Essentially no part of the program is typed, as with traditional development environments. A LabVIEW program is called a virtual instrument, or VI. The user should think of a VI as if it were another laboratory instrument. Each VI has a front panel and a block diagram. The front panel defines the user interface, while the block diagram defines the operation of the VI, much like a traditional laboratory instrument has a front panel and internal circuitry. The VI front panel contains controls, such as buttons, switches, and number entry fields, and indicators, such as LEDs and text display fields. Controls allow input from the user; indicators display information. More complicated controls and indicators, such as waveform plots, are also available. Controls and indicators may be customized in any number of ways, including with labels and data range restrictions.

107 94 The VI block diagram functions much like a circuit diagram. Each control or indicator on the front panel is represented by a small symbol, called a block, on the block diagram. On the block diagram, the developer may also place function blocks, which perform computation and data manipulation functions but do not have a user interface element on the front panel. Each block has one or more terminals. The block terminals are connected together by wires that represent the flow of data. For cases where constant data values are needed, the developer can place constants on the block diagram. Constants function like controls, except they have no front panel component, and their value is specified by the developer. A simple example of a LabVIEW program is a VI that adds two numbers, multiplies the sum by a third number, and displays the result. The VI has three numeric controls and one numeric indicator on the front panel. The block diagram consists of the front panel blocks plus one Add function block and one Multiply function block. Two controls are wired to the inputs of the Add block. The Add output and the third control are wired to the inputs of the Multiply block. The Multiply output is wired to the numeric indicator. When the user enters numbers in each of the controls and presses the Run button on the toolbar in the VI s front panel window, the result is displayed in the indicator. The power of LabVIEW resides in its extensive set of function blocks. Simple mathematical functions, such as addition and exponentiation, are of course available. Traditional programming structures, such as loops and decision statements, are available as blocks (including for, while, and case structures); these structures are large and

108 95 resizable and can contain any number of inputs, outputs, and other function blocks. Comparison blocks return Boolean results that allow decisions to be made. Many function blocks are available that provide operating system interfaces, such as file input/output blocks and network interface blocks. GPIB communication is performed through GPIB function blocks. Structures provide a great deal of the interactive capabilities of LabVIEW. Case structures replace the if-then statements of sequential programming languages. A case structure is a large frame with a selector input. The selector may be a Boolean, making the case structure function as an if-then statement, or any other kind of data type, making the case structure function as a case or switch or select statement. Blocks are placed inside the frame that correspond to the different functions to be executed for different cases. One case is displayed in the frame at a time, much like the pages of a note pad. A single case can handle one or more selector values. A single case may be identified as the default case; if the selector has a value that is not covered by other cases, the default case is selected. The developer may connect other inputs and outputs to the case structure; the blocks placed in each individual case must each provide a value for each output from the structure. Loops are implemented as both for loops and while loops. A for loop executes a fixed number of times (e.g., for each element in an array). A while loop executes until a Boolean condition becomes false (i.e., while a condition is true). The function blocks placed within the loop structure do not change, as with a case statement. However, the iteration count of the loop is available as a variable, and more advanced loop features

109 96 such as tunnels, shift registers, and feedback nodes allow values to be propagated from one loop iteration to another. Naturally, a loop structure may have data inputs and outputs, just as a case statement. Other kinds of execution structures are available in LabVIEW. Event structures are primarily used for advanced user interface processing; they function similarly to case structures, with one case for each possible user interface event. Formula nodes allow the developer to type a complicated calculation as an expression in a syntax similar to the C programming language. MATLAB script nodes function like formula nodes but call MATLAB to process the script contained in the node. When developing large programs, it is common practice to put logically separable or often-used subprograms into separate functions or separate files. LabVIEW emulates this practice by allowing the developer to create a subvi. A subvi is simply another VI. It has a front panel and a block diagram. When the subvi block symbol is placed on the block diagram of another VI, the controls and indicators on the subvi front panel act as the block s inputs and outputs, respectively. The example VI described above could be used as a subvi by placing it on the block diagram of another VI; the three numeric controls and the numeric indicator would be represented on the block diagram by three input connections and one output connection, respectively. Multiple VIs can be stored in a VI library, a compressed file that contains a set of VIs LabVIEW Execution The most complicated aspect of LabVIEW development is understanding the execution of the VI. Typical text-based programs have an obvious execution order, i.e.,

110 97 top to bottom, with branches and loops indicated in the source code. However, LabVIEW VIs attempt to emulate laboratory instruments and are graphical in nature. The block diagram, similar to a circuit diagram, seems to dictate that all things are happening simultaneously. The key to understanding LabVIEW VI execution is to compreh how LabVIEW maps an apparently simultaneous diagram into sequential computer execution. The best reference for this information is [19]. The process of gaining this comprehension is aided immensely by the LabVIEW Highlight Execution option, wherein the block diagram is highlighted during VI execution with small dots representing data flow. The basic element of VI execution can be thought of as the command, Do everything on this block diagram once. Each function block is executed once. A control executes by transmitting its data value along the wire connected to it; an indicator executes by absorbing a data value from its wire and displaying it for the user in an appropriate format. A function block or subvi executes by taking its inputs, performing its appointed function, and generating outputs; these output values are transmitted down the output wires. When one block s input is connected to another block s output, the latter block is guaranteed to execute before the former. A block cannot execute until data values have been transmitted to each of its inputs. Blocks that have no relative depencies, or blocks with no inputs, may execute in any order; execution order is not guaranteed. An brief analysis of the simple example above is helpful. The front panel of a VI is always live, i.e., the controls can always be manipulated, even when the VI is not

111 98 strictly executing. The user enters three numbers in the three controls and presses the Run button on the toolbar. At this point, execution begins. The VI executes by using the pseudo-command Do everything on this block diagram once. The indicator cannot execute until the Multiply block has executed. The Multiply block similarly waits for the Add block, and the Add block waits for its two numeric controls. The controls have no inputs and can execute first. Once the controls have transmitted their data values, the Add block can execute. When the Add block has finished, the Multiply block has its two inputs and can execute. Finally, the Multiply block transmits its output value to the indicator, and the indicator displays the result for the user. Although this is a simple example, some of the finer points of execution order can be demonstrated. First, note that each of the controls is indepent of the other, so the controls themselves can execute in any order. The third control, connected to the Multiply block, may transmit its value before either of the other controls executes. (The transmitted value would then be stored at the input of the Multiply block until all inputs are available and the block executes.) Conversely, the first two controls and the Add block may execute before the third control executes. Since the Add block and the third control are indepent of each other, they may execute in any order. The only guarantee is that the Multiply block will execute after the Add block and the third control have both finished executing. The execution of case and loop structures is similar to that of the block diagram. When all of the input values, including the selector value, have arrived at a case structure, the structure executes by choosing the appropriate case and then executing its function

112 99 blocks. One way to think about this execution is that the case selector decides which case to use, and then execution continues as if the blocks in that case were placed directly on the block diagram. Loop execution is similar. A loop structure executes by executing its contents an appropriate number of times. It executes as if, instead of a loop with N iterations, the loop contents were repeated on the block diagram N times. The output of a loop structure is not transmitted until the final loop iteration has completed execution. It was noted earlier that, when the Run toolbar button is pressed, the VI executes its entire block diagram once and then s execution. In order to provide a more interactive experience, most VIs inted for interactive use have a main, outer while loop and a Stop button. The VI continues to execute until the user presses the Stop button. The loop usually contains a Wait (ms) function block configured to wait for a short time, typically around 100 ms. In this way, the VI essentially re-executes every 100 ms. Any updates to the controls produce instant results. Controls and indicators are placed inside the main loop on the block diagram so their values are read and updated every time the loop executes. A common, alternative structure for interaction is an event structure inside a while loop. When the event structure executes, it waits for a recognized user interface event to occur. (User interface events that the event structure is not configured to handle are not recognized.) When the event occurs, the event structure executes the corresponding event case. When the event case completes, control is returned to the while loop. If the user has pressed the Stop button, the loop completes execution, and the VI terminates. Otherwise, the loop executes again, and the event structure executes again, waiting for a

113 100 recognized event to occur. Event structures are somewhat more complicated but provide a smoother user interface. The control program for the present experiment uses an event structure inside a while loop. Event structures may be exted to cover event types other than interface events through the use of user events. Most event messages are generated automatically by LabVIEW as a result of user interaction. A user event is a custom event message generated by the program. As an example, a VI front panel might have numeric controls labeled Amplitude and Frequency, as well as several indicators whose displayed values dep on the values of those controls. The developer might choose to create a user event named Recalculate Display Values. The VI would first register this event, and then an event structure would be configured with a case to handle the event. In the VI event structure, the developer would create cases to handle the Amplitude: Value Change and Frequency: Value Change messages. In each of those cases, the developer would place a block to generate the Recalculate Display Values event. When the value of the Amplitude field is changed, LabVIEW will automatically generate the Amplitude: Value Change event message and place it in the event queue. When the VI s event structure handles this message, it will perform any necessary functions and then place the Recalculate Display Values event message in the event queue. Once processing for the Amplitude: Value Change event has completed, the event structure returns control to the outer loop; on the next iteration, the event structure reads the Recalculate Display Values message from the event queue and processes it. Events used in this way allow common processing to occur for several different events.

114 3.6 The Vapor Cell Experiment LabVIEW Program 101 The Vapor Cell Experiment (VCE) LabVIEW program is a LabVIEW VI that was written to run the SR430 repeatedly, retrieving the trace data after each run. After the user specifies experiment settings, the VCE VI runs the experiment and retrieves the SR430 data. The VI then repeats the cycle. Each run-finish-read cycle is called an experiment cycle, or simply a cycle. Any number of cycle may be specified. The data retrieved from the SR430 is stored in a MATLAB native format using the LabVIEW MATLAB interface. The VI will optionally process the data before storing it. Records are kept of the experiment settings, date and time of execution, and results. Running optimally, the experiment can run at a repetition rate of approximately 3 Hz, or 3 experiment cycles per second. The VCE VI is the top-level VI in a VI library. The library consists entirely of VIs custom-written for this purpose. The VCE VI also relies on another VI library, the SR430 instrument driver library. An instrument driver is a VI or collection of VIs that provide simplified access to an instrument. For example, an instrument driver provides one function block for each instrument command. Instrument drivers hide some of the complexities of GPIB interfaces. The SR430 instrument driver is available from Gesellschaft für Schwerionenforschung mbh (Association for Heavy Ion Research) in Darmstadt, Germany. The GSI SR430 instrument driver is freely available under the terms of the GNU General Public License. Several additional SR430 interface function blocks were developed during the course of the experiment, particularly function blocks needed to retrieve settings from the SR430. They are not strictly part of the GSI

115 instrument driver per se, but they fit the general pattern of GSI functions and were added to the experiment copy of the GSI library to maintain consistency User Interface The VCE VI interface is shown in Figure 34. Toward the upper-left corner of the front panel are the main experiment settings. In the upper-right corner are some additional settings that are rarely used. In the left middle region are text and filename entry fields, and in the right middle region are the activation buttons. Toward the bottom of the front panel are status indicators and some seldom-used buttons. The LabVIEW Context Help window, if open, displays information relevant to the control or indicator over which the mouse cursor is positioned. The Experiment type selector allows the user to choose the kind of experiment to run. This primarily affects post-processing of the SR430 data. Available types are Raw data, Start-stop, and Number corr., meaning number correlation. The Raw data experiment type runs the SR430 and retrieves the complete data trace after each scan. The entire data trace is saved to the data file; if multiple cycles are run, each trace is saved as a column of the data matrix. The Start-stop experiment type does not save the entire trace, but rather counts the number of time bins between the first and second pulses and saves that number instead of the entire data trace. Multiple cycles lead to multiple numbers stored in a vector. The Number corr. experiment type sums all of the counts over two windows; it is expected that the windows will correspond to the write and read pulses. The number of photon counts in the write pulse window and the number

116 103 of photon counts in the read pulse window are saved to the data file. A multi-cycle Number corr. experiment results in a two-row data matrix. The # cycles field determines the number of times to run the experiment, or the number of data traces to collect. The # records/scan, Bin width, and # Kbins correspond to the equivalent SR430 settings. The Total scan time field is computed from the bin width and bin count fields. If a value is entered into the Total scan time field, the bin count is recomputed. The Read params button causes the VI to access the SR430, read the three parameters, and update the fields with the SR430 s current values. The First pulse offset, First pulse duration, Second pulse offset, and Second pulse duration fields are only used by the Number corr. experiment type and are disabled (grayed out) when other experiment types are selected. These fields determine the windows over which photon counts are summed. The pulse offsets and durations are specified in terms of zero-based bin number. The corresponding times are based on the selected bin width and are referenced to 0 s as the start of the data trace. If a value is entered into any of the time fields, the corresponding bin number is recomputed. The GPIB address field specifies the GPIB address of the SR430. The default address for the SR430 is 8. Valid addresses range from 1 to 31. If multiple GPIB controllers are present in the PC, the address format X : Y is used, where X is the controller number (starting from zero) and Y is the device address on the specified controller. The Manual name pushbutton overrides the automatic data file naming used by the VI. For general operation, the Manual name button should be turned off; only exceptional circumstances warrant the use of this feature.

117 104 The Data filename field allows entry of a data filename. Data files use the file extension.mat, as they are MATLAB native format files. The default folder for data files is a subfolder named for the current date (e.g., ) in the Vapor Cell Experiment\Data folder. When the VI is opened, if the default folder does not exist, the user is asked whether it should be created. The default data filename is VCxx.mat, where xx is replaced by the lowest unused number in the folder (meaning the lowest number that produces a filename that does not already exist). The VCE VI uses automatic data file naming to avoid overwriting existing data files and to create a log of all data recorded on a given day. The automatic file naming feature uses numbered file names. The user may select a base name for the file, such as Test data 001.mat. The VI will automatically increment the number at the of the filename until it finds find the next available number in the specified folder. For example, if fifteen similarly-named, consecutively-numbered files were found in the data folder, then when the user typed Test data 001.mat (or selected it from the file browse box, activated using the ellipsis pushbutton near the Data filename field), the VI would automatically change the data filename to Test data 016.mat. (When generating the filename, the VI uses at least as many digits as are present in the specified filename.) When the experiment is run, the data will be saved to this data file. Shortly after the experiment completes, the VI will increment the filename again to Test data 017.mat. This is the recommed behavior. In instances where this behavior is not desired, enabling the Manual name pushbutton will use the data filename as entered and not

118 105 alter it. The user is always prompted at the start of the experiment run before a data file is overwritten. The Description field allows the user to enter a text description of the experiment to be run; previous entries in the Description field can be selected using the arrow to the right of the field. This text field is used to generate the Full description field, which is written to the data file, the Readme file, and the log file. The Readme file is a text file named Readme.txt in the same folder as the data file; it contains one-line descriptions of the data files in the folder. A new description (using the value of the Full description field) is apped to the file every time an experiment is run. The log file is a text file named VC Log.txt in the same folder as the data file. The log file contains the exact starting and ing times of the experiment run, as well as detailed information about any errors that occurred during the experiment and whether the user cancelled the experiment run. The names of these files cannot be changed by the user, and they always reside in the same folder as the data file. The Run button runs the experiment for the specified number of cycles. When this button is first pressed, most of the controls on the front panel are disabled. The SR430 is initialized with the specified parameters, and then the SR430 scan is started. When the SR430 scan is complete, the VI reads the trace data from the SR430 and restarts the scan, continuing as many times as specified. As each cycle is completed, the Cycles completed field is incremented. The End now button allows the user to the experiment before all cycles are completed; any data retrieved is saved to the data file. When the experiment run is completed (or ed early), the Run button resumes its

119 106 deselected state, the data filename is incremented (unless Manual name is selected), the front panel controls are re-enabled, and the VI returns to its initial state. The Get data button retrieves the current trace data from the SR430 without initializing it or initiating a scan. The data trace is saved to the data file, and the data filename is incremented, just as with the Run button. This is useful when the user has operated the SR430 manually and wishes to capture the data trace to a file on the PC. (Pressing the Get data button also causes the VI to retrieve the current SR430 settings, as with the Get params button, so that a correct description can be written to the data file.) Other user interface elements are seldom used but should be self-explanatory. The Time stamp field indicates the time at which the experiment run was started (i.e., the time at which the Run button was pressed). The Status field indicates the ing time and status of the experiment run. Possible status values are Completed, Canceled, and Error. The EXIT button is used to the VI operation and close the window. Do not use the window close button or any other means to the VI. (To edit the VI for further development, use the Abort button on the toolbar.) The Reinitialize button reinitializes the VI front panel to its initial state. If the VI stops responding or is incorrectly disabled, the Reinitialize button should be pressed. If the SR430 stops responding to its own front panel, the Help button on the SR430 should be pressed to bring the SR430 out of remote mode. If the VI and SR430 appear to be operating normally but not communicating with each other, the VI should be closed, and the SR430 should be turned off; after approximately 30 s,

120 107 the SR430 should be turned back on, and then the VI should be opened again. It is not believed that any of these situations will arise during experimental operation of the VI and the SR430; however, during development of the VI, they were rather frequent occurrences, meriting a mention of the associated fixes Data File Format The data files written by the VCE VI are MATLAB native format binary files. These files are usually called MAT-files, since the file extension used is always.mat. MAT-files contain one or more variables, with name, type, size, and value all stored in the file. When the MAT-file is loaded from disk, using the load command in MATLAB, the variables are loaded into the MATLAB workspace. Using an alternate form of the load command, the variables may instead be loaded as fields in a structure. The variables stored in the file are the data variable, which contains the data retrieved from the SR430, and a several other variables that contain settings and other information. The data variable is a double-precision matrix of values containing the data read from the SR430. The number of columns in data corresponds to the number of cycles completed. For the Raw data experiment type, each column contains the full trace from the SR430. The number of rows will be an even multiple of 1024 corresponding to the number of bins per record. For the Start-stop experiment type, each column contains a single number, namely, the number of time bins between the first and second non-zero bins of the data. For the Number corr. experiment type, each column contains two numbers. The first number is the number of photons detected during the first pulse window, or write pulse; the second number corresponds to the

121 108 second pulse window, or read pulse. (Although the VCE VI will perform the computations needed to reduce the SR430 data to one or two numbers, it is also possible to run the Raw data experiment type and perform the computations in MATLAB.) The remaining variables in the data are informational and, with one exception, are all strings (i.e., character row vectors). description contains the value of the Full description field, including the SR430 settings. status contains the value of the Status field. dir is the full path of the folder where the data file resides, and file is the name of the data file with no path information. The full path to the data file can be reconstructed in MATLAB using the command fullfile(dir,file). The cycles variable is a doubleprecision scalar; it indicates the number of cycles that were requested by the user, which may be different from the number of cycles actually completed. The number of cycles completed is specified by the number of columns in the data variable VI Internal Structure The VCE VI s internal (block diagram) structure centers around an event processing loop, i.e., an event structure inside a while loop. The bulk of the program logic resides in the different cases in the event structure. User events are used to consolidate event handling logic, as discussed in LabVIEW Execution above. The only items located outside the event processing loop are the control and indicator blocks themselves (with few exceptions), some initialization logic, and the event registration blocks. The types of events handled by the event loop are Value Change events and user events. Value Change events are generated by LabVIEW in response to user

122 109 activity on the front panel, such as pressing a button or changing the value of a field. The Value Change event processing is straightforward in most cases; for most controls, the Value Change event is simply a trigger to generate an event to update the value of another control. For example, the # cycles and # records/scan values are used in the Full description field. A single event case handles Value Change events for both of these controls, and the event case simply generates a Compute full description user event to cause the Full description field to be updated. As an additional example, the # Kbins parameter is used in the Full description field and specifies the maximum value for the pulse offset and duration fields. The # Kbins: Value Change event case, therefore, adjusts the maximum values of the pulse parameter fields, generates a Compute full description user event, and generates a Compute times event to update the pulse parameter fields. The user events used in the VCE VI are as follows: Compute filenames causes the data, Readme, and log filenames to be updated. Compute times causes the Total scan time and pulse parameter time values to be updated from the corresponding bin numbers, or vice versa. Enable front panel enables or disables certain parts of the front panel, deping on the choice of experiment type and whether the VI is about to start or finish running an experiment. Compute full description generates a new value for the Full description field based on the current parameter settings. Read params causes the operating parameters to be read from the SR430 and updates the front panel with the new values. Get data retrieves the current data from the SR430, writes it to the data file, adds an entry to the Readme file, and updates the data filename when the front panel

123 110 button of the same name is pressed. (One important note is that, since the Get data operation first requires the VI to read the current SR430 settings, the Get data button actually generates a Read params event, which in turn generates the Get data user event.) Run experiment handles the mechanics of running the experiment, namely, initializing and running the SR430, retrieving the data, and writing the data, Readme, and log files. Many subvis were created to perform various functions within the block diagram. Most subvis perform a simple computation and return the results; for example, Adjust Pulse Parameters.vi takes in pulse offset and duration bin numbers, as well as the value of the # Kbins field, and returns offset and duration bin numbers that have been adjusted to fall within an acceptable range. A few subvis perform major, integrated functions; examples of such functions are Run Start-Stop Experiment Once.vi, Run Number Corr Experiment Once.vi, and Get SR430 Settings.vi. SubVI names should be self-explanatory, and the subvis themselves perform fairly straightforward functions Performance The maximum repetition rate that can be achieved with the VCE VI is 3 Hz. The VCE VI execution speed and the effective experiment repetition rate are limited primarily by the operation of the SR430. A timing analysis of VCE VI execution shows that, even at optimal settings of 1024 bins per record and a 5 ns bin width, the SR430 requires approximately 250 ms to complete an entire scan cycle and approximately 70 ms to transfer the data record to the PC. The time required by the VCE VI for one complete experiment run is roughly 10 ms to 30 ms. The maximum trigger rate of the SR430 is

124 111 listed in the product manual as 2400 Hz and is only achievable with the settings specified above. However, it appears that this rate applies only to the case of multiple records per scan. Additional time may be needed for the SR430 to transfer trace data from data acquisition memory to display memory, or the memory from which the GPIB data is read. Display memory is discussed in greater detail in the SR430 product manual. It should be noted that, although the repetition rate is limited to around 3 Hz, the trigger rate can be 10 Hz or even higher. When multiple records per scan are requested, a higher trigger rate will reduce data collection times, as the VCE VI does not require access until the scan is complete. In the case of a single record per scan, scans are initiated by the VCE VI, and the SR430 will ignore excess trigger pulses. For the present experiment, 3 Hz is a sufficiently high repetition rate to make the required data recordings in a reasonable amount of time. 3.7 Computer-Aided Analysis All plotting and analysis for the experiment were carried out using the MATLAB environment from The MathWorks. A series of MATLAB programs were developed to read in, manipulate, and plot data. These programs were written as M-files, so called because of the file extension.m. A very brief description of the more important M-files follows. More information is available within the M-file source code. Descriptive help text is usually available from within MATLAB by typing help followed by the command name.

125 Data Import Commands Data traces saved on the TDS 3012 digital oscilloscope are typically saved in the Tektronix internal format with a file extension of.isf. These files can be read into MATLAB using the read_tds3000 command. This command returns a column vector of the recorded voltage value of each point in the oscilloscope data trace. It will optionally also return a column vector of equal length containing the time value of each data point relative to the oscilloscope trigger and a MATLAB structure containing the oscilloscope settings listed in the data file. The command accepts an option to plot the data after reading it from the data file. The read_tds3000 command is extremely robust and should be able to parse data files correctly from any modern Tektronix digital oscilloscope, including those from other than the TDS3000 series. When SR430 trace files are saved to floppy disk, they are saved in the SR430 internal file format, typically with no file extension. The data in these files can be loaded using the read_sr430 command. read_sr430 returns the count in each bin as a row vector. As with read_tds3000, read_sr430 can optionally return the relative time of each data point and a MATLAB structure containing the instrument settings listed in the data file and can plot the data after reading it in Plotting and Analysis MATLAB has extensive data plotting capabilities, and these were utilized quite thoroughly in the present experiment. Several M-files were written to automate major parts of the plot generation process and to afford some convenience in analysis. However, these M-files were not inted to generate the plots entirely without user intervention.

126 113 As such, automatically plots are saved as MATLAB figure files (with a file extension of.fig) and typically hand-tuned afterward. (The general rule mentioned previously was followed; namely, if the development, testing, and use of a system required less time in total than manual execution of the same tasks, the M-file would be developed, and not otherwise.) The primary plotting function used in the experiment is the fpplot command. It was originally written for interactive generation and analysis of plots of Fabry-Pérot spectrum data, both from the oscilloscope and from the SR430. However, many of its features are broadly applicable, allowing it to be used more generally. Typically, the arguments passed to the command are filenames or filename specifications to be plotted. Wildcards may be used, namely, * (asterisk) to represent any number of characters, and? (question mark) to represent precisely one character. At the MATLAB command prompt, these names may be typed directly after the command name, separated by spaces and without quotes or parentheses. For example, fpplot *.isf will load and plot all oscilloscope data files in the current folder. The user can scroll through the plots using the arrow keys, and several other features are available. Perhaps the most important additional feature is the binning of data. When a large number of bins per record are specified on the SR430, consecutive groups of bins may be summed to provide a smoother data trace. In particular, one interactive command changes the plot between displaying each bin and displaying sums of every 16 bins. The fpplot command also has a non-interactive mode for automated generation of plots. More information on fpplot is available through the MATLAB help command and from the interactive menu.

127 114 Many times, the user wishes to mark the relative frequencies of the peaks on a Fabry-Pérot plot. The add_peaks command offers this feature for pre-existing plots. It is an interactive tool that allows the user to select the location of several peaks manually and automatically determines the relative frequencies of the peaks (based partly on user input). The peaks are labeled with vertical lines and text labels. The figure file can be saved; later, the command get_peaks retrieves a list of these labeled peaks, and the command find_peaks can find the maximum-value data point near each peak marker line. The command rescale_peaks allows the frequency axis of a frequency-marked plot to be rescaled slightly and updates the peak label text with the newly-computed frequency. One additional MATLAB command, html_doc, was written and is available to aid in analysis. After large amounts of data were collected, it became somewhat difficult to locate important data files after their collection. Each data file is uniquely named and stored in a folder named for the date of collection (e.g., ) in the Vapor Cell Experiment\Data folder on the PC. A file named Readme.txt containing a one-line description of each data file is kept in virtually all such data directories. However, after data had been collected for many months, individual data files were nevertheless hard to locate. To this, the html_doc command generates two HTML files in the Vapor Cell Experiment\html folder. The first file, named index.html, contains a listing of every file and subfolder at every level beneath the Vapor Cell Experiment folder on the PC. Text files, particularly Readme.txt, are copied in their entirety into the HTML file. M-files are coupled with a one-line description of the function performed by the file (taken from the first comment line of the file, called the H1 line in MATLAB).

128 115 For all recognizable data, figure, or image files, the files are plotted or displayed, and html_doc generates both a full-size image and a tiny snapshot of the result. In the HTML file, next to the filename, a reference to the snapshot image is placed, along with a link to the full image; a user who clicks the snapshot will see the full image. In this way, the user can browse the Vapor Cell Experiment folder and its subfolders with some idea of the contents of the files. The second HTML file, images.html, simply contains all snapshot images placed side-by-side with no intervening text and linked to the full-size snapshots. This allows easy browsing and searching of plots and images. html_doc intelligently generates only those images that have not been generated or whose sources have been updated, particularly since the tiny and full-size snapshots take several minutes to generate. html_doc skips any folders it finds named html, primarily to avoid recursion RS-232 Instrument Control When it became clear that computer control of instrumentation would be necessary, the obvious first choice for development environment was MATLAB. MATLAB is flexible, efficient, largely user-frily, and already was used exclusively for data analysis. A MATLAB instrument control interface would allow seamless retrieval of data and experiment execution control alongside the existing data analysis features. The MathWorks offers an Instrument Control Toolbox for MATLAB that offers both GPIB and RS-232 interfaces. Partly as a consequence of IEEE Standard 488, the interfaces work nearly identically from within MATLAB. The Instrument Control Toolbox would offer an ideal choice for experiment control, allowing the development

129 116 initially over RS-232 and then offering an easy upgrade path to GPIB later when higher data transfer rates were needed. Costs for MATLAB Toolboxes are often prohibitive, except where they are directly pertinent to the kinds of data analysis performed. In this case, cost was an overriding factor, and the Instrument Control Toolbox was not purchased. The RS-232 serial interface portion of the Instrument Control Box is included as a standard part of MATLAB. This was pursued as a possible avenue for experiment control. The serial interface features built into MATLAB were used in an attempt to control the SR400 photon counter and the SR430 scaler/averager. Some success was achieved; however, both instruments are limited to a maximum serial bit rate of bit/s. With standard communications settings, and considering RS-232 framing overhead, that equates to a typical maximum data rate of 1920 B/s. (Using uncommon but allowed communications settings, an absolute maximum data rate of 2133 B/s is possible.) More importantly, the serial interface was determined to be unreliable. Bytes are sometimes lost, altered, or inserted into the data stream, and it is not always clear when any of those events has happened. The cause of serial unreliability is unknown. The SR400 and SR430 could very conceivably have identical RS-232 control circuitry; if the circuits used by Stanford Research are erratic, then the same problems could be exhibited by both devices. At the same time, the MATLAB serial interface on the Windows platform is based on the Java serial port interface for Windows. Java is known to be unreliable and unstable, and the Java serial port interface has reliability issues. The MathWorks has made available a patch for MATLAB revision 13 that addresses some of

130 117 these Java serial reliability issues; however, it is not known whether the patch fixes all serial issues. The net effect is that, although somewhat sophisticated and flexible control software was implemented in MATLAB, the MATLAB instrument control software is not used in the present experiment.

131 118 APD Coupling lens Shielding barrel Iris Attenuator wheel (x2) Flip mirror Fabry-Perot Cavity Multimode fiber Photodetector (a) HV piezo input TDS3012B Oscilloscope 1 2 T DS345 Function Generator 10 Hz HV Amplifier 10x probe From photodiode To Fabry-Perot HV piezo input To Pulse Generator trigger input SR400 Photon Counter SR430 Multichannel Scaler 12, T 1 T From APD output (b) Figure 27. Detection system block diagram.

132 HV ramp Linear fit 250 Ramp voltage (V) Ramp time (s) Figure 28. High voltage ramp distortion.

133 APD box Coupling lens box 120 Felt Beam Optical fiber (a) Coupling lens Attenuators Iris (b) Figure 29. Shielding for APD and fiber coupling lens.

134 To APD gate input 121 TTL gate signal 2N Ω Figure 30. APD gate switching circuit.

135 Arbitrary scale 0.5 Mirror images Mirror images Time (s) Figure 31. Fabry-Pérot ramp mirror image.

136 Figure 32. Pulsed-mode excitation timing diagram. 123

137 Figure 33. APD dead time. 124

138 Figure 34. Vapor Cell Experiment VI front panel. 125

139 Chapter 4: Experimental Results 4.1 Summary of Results A number of interesting results have already been obtained during the course of the present experiment. Both Stokes and anti-stokes lines have been observed, even at classical light levels, in 85 Rb. The absorption spectra of the heat pipe vapor cell, the mixed-isotope glass vapor cell, and the pure-isotope glass vapor cell have all been recorded experimentally. At low light levels, multi-spectral gain was observed even beyond what was seen at classical light levels. The effects of optical pumping were studied. Promising initial results were obtained for the pulsed excitation mode, demonstrating that the current experimental apparatus will be sufficient for observing the desired effects in the pulsed excitation mode. 4.2 Classical-Level Results Anti-Stokes Generation at Classical Levels The data collected during Phase I of the experiment focused on spectral resolution of the Raman pump and probe. Figure 35 shows a collection of typical data traces for the experiment. It is intriguing that both Stokes (probe) and anti-stokes lines are visible, as the Raman-resonant third-order susceptibility predicts the presence of only the Stokes line. In this case, the anti-stokes line can be explained by a phase-matched nondegenerate four-wave mixing process. The four-wave mixing process is a result of the 126

140 127 third-order susceptibility of the Raman vapor medium interacting with the pump and probe fields. The pump acts as ω 1 and ω 2, the probe acts as ω 3, and the anti-stokes line is generated as ω 4. In effect, the pump is acting on both the 85 Rb 5 2 S 1/2 F = 2 and F = 3 levels simultaneously; the probe and pump cause transitions from F = 2 to F = 3, and the pump causes transitions from F = 3 to a virtual level, causing 85 Rb atoms to emit the anti-stokes photons while returning to the F = 2 level. It should be noted that, because of the phase-matching condition, the anti-stokes beam propagates at a very shallow angle relative to the pump and probe beams; however, the angle is shallow enough that the beam still lands on both the classical detector and the APD fiber coupling lens, even after propagation along the optical table. Figure 36 shows the heterodyne beat note between the probe and anti-stokes lines at roughly 6.07 GHz, or twice the ground-state splitting of GHz. Both the probe and the anti-stokes line were found to be polarized perpicular to the pump. The probe gain is approximately 6 db, and the anti-stokes line intensity can be made as large as about 8% of the input intensity. The exact frequency shifts and relative intensities of the Stokes and anti-stokes lines vary with the Raman pump intensity and detuning and the optical pump intensity; these effects were studied in greater detail using low photon count light levels Vapor Cell Absorption Spectra The experimental setup was used to verify and record the absorption spectra of the three Raman vapor cells (heat pipe cell, mixed isotope glass cell, and pure isotope glass cell). Figure 37 shows the saturated absorption spectrum of mixed-isotope

141 rubidium. Figure 38 shows part of the absorption spectra of the three vapor cells used in the experiment. The red curve shows the linear absorption for the mixed-isotope cell. The green curve shows the linear absorption in the pure-isotope cell (note the missing 87 Rb absorption line). The blue curve is a typical, mixed-isotope saturated absorption curve that has been shifted by 1.1 GHz to represent the detuned pump. Note that, as expected, the mixed-isotope cells show absorption lines from both 85 Rb and 87 Rb, while the pure-isotope cell shows only the lines for 85 Rb. For these readings, the oscilloscope was set to accumulate a number of traces and display the average of those traces. 128 Optical pumping is used for population transfer from the F = 3 to the F = 2 level. In order to verify the optical pumping effect, an absorption spectrum trace was taken. As described in the Experiment Description chapter, optical pumping was performed using a fixed frequency from the second laser, while the first laser was scanned over the appropriate frequency range. Figure 39 clearly shows population transfer out of the 85 Rb F = 3 line. There is virtually no absorption at the F = 3 line, as all of the 85 Rb atoms in the vapor medium have been pumped into the F = 2 state and are transparent to photons at the D2 F = 3 transition frequency. 4.3 Spectrally Resolved Photon Counting Phase II of the experiment focused on studying the behavior of the vapor medium under low-light conditions. The Raman pump power are reduced, and the probe beam is blocked entirely (except when used as a frequency reference). The APD is used for photon counting, and the Fabry-Pérot cavity resolves the signal spectrally. Figure 40 shows a typical spectrally resolved trace. The pump is suppressed by the polarization

142 129 filtering and the absorption cell. Even at a reduced light level, the Stokes and anti-stokes lines from 85 Rb are apparent in the trace. Their frequency separation is measured as approximately 6.08 GHz. (Peak locations for measurement purposes are determined manually.) Figure 41 shows the relative intensities of the Stokes and anti-stokes lines for different pump intensities. The spectral peaks in Figure 40 are asymmetric and slightly broader than the Fabry-Pérot line with of approximately 260 MHz; it is presumed that these effects are caused by an asymmetric transverse pump beam profile, which in turn causes inhomogeneous power broadening in the vapor medium. Fabry-Pérot cavity misalignment can produce similar effects but was ruled out based on careful alignment and the use of back-reflections from the cavity. Nonlinear response of the high-voltage amplifier and piezoelectric crystal is also ruled out, as the same broadening and asymmetry are seen equally in all parts of the spectrum Multi-Spectral Raman Gain Many additional spectral lines are present in the trace shown in Figure 40, beyond even the Stokes and anti-stokes lines observed in Phase I of the experiment. Some of these lines may be explained by the light shift effect, or AC Stark effect. As the pump field intensity is increased, the high-intensity field causes level splitting in the atom, and small satellite lines shift away from the main lines. In this case, since the Raman pump is red-detuned, the lines shift toward lower frequencies. Figure 42 shows a linear-fit plot of the measured shift of these lines for different pump intensities. More information about the AC Stark effect can be found in [5].

143 130 These light-shifted lines and the other newly appearing lines in Figure 40 have been investigated theoretically using a numerical simulation. The results of the simulation indicate that, aside from light-shift-induced lines, all lines in the spectrum can be identified as Stokes or anti-stokes lines from pump-induced transitions in both 85 Rb and 87 Rb. Figure 43 shows the simulation results compared to actual experimental data. Coincidentally, the free spectral range of the Fabry-Pérot cavity of approximately 15 GHz happens to match the 87 Rb Stokes-anti-Stokes frequency separation of 13.6 GHz almost exactly. As a result, the 87 Rb Stokes and anti-stokes lines overlap and appear as a single line in the plot in Figure 40. For verification purposes, the Fabry-Pérot free spectral range was increased to approximately 27 GHz; a spectral resolution at that free spectral range is shown in Figure 44. That figure also shows the effects of pump detuning on the relative intensities of the spectral lines. It is noteworthy that all of the effects seen here result from excitation of the vapor medium by a single pump frequency. Pump-induced Raman transitions in 85 Rb generate the Stokes frequency, and the pump and newly generated Stokes fields cause the generation of the anti-stokes frequency. A similar process is believed to happen simultaneously in 87 Rb, accounting for the presence of both Stokes and anti-stokes lines in that isotope. Further, high pump field intensities can induce light shifts in atoms of both isotopes. A single pump beam produces as many as eight distinct fields, each at a different frequency from the others.

144 Effects of Optical Pumping Figure 40 shows the spectral effects of optical pumping for normal pump detuning. Optical pumping and the resulting population transfer increase the intensity of the emitted 85 Rb Stokes line. Although the 85 Rb anti-stokes intensity is reduced, it is not reduced much, due primarily to alignment difficulties between the optical pumping and Raman pump beams. The other lines seen in Figure 40 also increase in intensity; backreflections of the strong optical pumping beam within the vapor cell are the likely cause of this increase Isotopically Pure Line Spectrum Although the multi-spectral gain effects seen in the mixed-isotope cells are striking, they represent a source of loss rather than a tool for certain applications, most notably the quantum memory and quantum entanglement source. Once the various effects seen in the line spectrum are clearly understood, one would expect that the isotopically pure 85 Rb vapor cell would exhibit only the effects attributable to 85 Rb. Figure 45 and Figure 46 show precisely that behavior. Under weak pump excitation, the isotopically pure vapor cell used in Phase III of the experiment emits only the 85 Rb Stokes and anti-stokes lines. 4.4 Pulsed Excitation Some initial results have already been achieved from Phase III of the experiment. This phase uses the pulsed excitation mode of operation and the isotopically pure 85 Rb Raman vapor cell. Figure 47 consists of an oscilloscope trace showing the effects of

145 optical pumping. The falling edge of the optical pumping pulse is shown, as well as the fluorescence from the vapor medium. While the optical pumping pulse is active, it functions much like a continuous-wave beam, exciting transitions in the atoms and stimulating the emission of photons as the atoms are excited into the F = 2 state. After the optical pumping pulse is switched off, the atoms decay randomly into the F = 3 state due to decoherence processes. Eventually, the atoms reach thermal equilibrium, being distributed between the F = 2 and F = 3 states, and no further fluorescence from the 132 vapor cell is observed. Figure 47 shows an excited state lifetime of approximately 500 ns. (To obtain the data for this figure, the Fabry-Pérot cavity was locked to a particular frequency, allowing the separate acquisition of the optical pump pulse data and the cell fluorescence data.) Figure 48 suggests the kind of data that is expected using the APD and SR430 with pulsed excitation. For this figure, the write beam (i.e., the Raman pump) was pulsed for approximately 0.04 ms, and no optical pumping pulse was used; the Fabry-Pérot cavity was removed from the beam path. The curve labeled Envelope shows the rough envelope of the write pulse. The curve labeled Pulse detected by APD shows the actual photon count data received at the APD; note the random photon arrival time. (Before the Fabry-Pérot cavity was removed from the beam path and this data was recorded, the photons seen in this figure were verified to be Stokes photons at the probe frequency; the write pulse photons are filtered and absorbed before they reach the APD.) The curve labeled Pulse detected by APD shows the photon count data accumulated over 100 records. The line labeled Low-intensity pulse shows the photon count data from a

146 133 single record. 18 photons were recorded during the Raman pulse on that particular trace; the ultimate goal is to reduce the write pulse strength and duration until, on average, less than a single photon is recorded by the APD per pulse sequence. Figure 49 shows the operation of the pulse sequence and the fluorescence detected during pulsed excitation. The vertical scale shows photon counts per 5 ns bin, while the horizontal scale shows the bin number. Figure 49(a) shows the last 2 µ s of the optical pumping pulse with the write and read pulses blocked. Figure 49(b) shows only the write pulse; in this case, the write pulse is expanded to 3 µ s to allow clearer observation of its effects. Figure 49(c) shows the optical pumping and write pulses together, separated by approximately 200 ns. Figure 49(d) shows the optical pumping and write pulses again, only with the write pulse intensity significantly reduced.

147 Ramp probe (no gain) amplified probe optical pumping magnitude (a.u.) anti-stokes image pumpleakage anti-stokes time (sec) Figure 35. Stimulated Raman gain, FSR of 15 GHz.

148 Heterodyne signal (dbm) Frequency (GHz) Figure GHz beat note between Raman anti-stokes line and probe line.

149 136 Transmission Rb 87 F=2 Rb 85 F=2 0.2 Rb 85 F= frequency (GHz) Figure 37. Saturated absorption spectrum for mixed-isotope cell.

150 New cell 6 5 Normal cell 4 3 Saturated absorption Figure 38. Absorption spectra for three vapor cells.

151 138 6 No optical pumping Counterpropagating optical pumping magnitude (a.u.) F=3,Rb F=2,Rb Scan time (sec) Figure 39. Population transfer with optical pumping.

152 GHz GHz Probe Anti-Stokes 1500 Photon count Relative frequency (GHz) Figure 40. Single-photon, spectrally resolved trace showing multi-spectral gain.

153 Stokes/Anti-Stokes Peak Count Ratio Incident pump power (mw) Figure 41. Stokes (probe) vs. anti-stokes intensity.

154 frequency (GHz) Left probe Right probe Pump power (mw) Figure 42. Light shift with increasing optical pump power.

155 1 x 10-9 Generated Frequency components, P = 1 mw S Rb 85 AS Rb S Rb 87 AS Rb 87 magnitude New Rb 85 line Rb 85 Rb frequency (GHz) P ~ 5 mw, FSR = 30 GHz Photon count (per 5.12 µs bin) Rb 87 S Rb 85 S Rb 85 As Rb 87 As Scan time (s) Figure 43. Simulation results compared to experimental results.

156 143 Averaged photon count (per 5.12 µs) δ = 1.1 GHz ( 85 Rb) δ = 0.2 GHz ( 87 Rb) 87 Rb S 85 Rb S (Probe) 85 Rb A-S 87 Rb A-S Relative frequency (GHz) Figure 44. Stokes and anti-stokes powers for different detunings.

157 144 Photon count per 5.12 µs bin Probe Pump incompletely absorbed Pump fully absorbed Pump Relative frequency (GHz) Figure Rb spectrum with 27 GHz FSR.

158 145 Photon count per 5.12 µs bin Probe Pump incompletely absorbed Pump fully absorbed Pump Relative frequency (GHz) Figure Rb cell lines.

159 population decay optical pump pulse magnitude pulse duration (sec) x 10-6 Figure 47. Population decay after 0.5 ms optical pumping pulse.

160 Pulse detected by APD 15 Envelope Photon count Low-intensity pulse Time (µs) Figure 48. A typical pulse, as recorded by the APD.

161 (a) (b) (c) (d) Figure 49. Pulsed-mode excitation.

162 Chapter 5: Theory 5.1 Raman Effect in an Atomic Ensemble The derivation of a quantum-mechanical representation of the Raman effect is desired. The system shown in Figure 50 is used for the derivation. The system consists of a pump laser, a three-level atom, and an optical cavity mode. The pump field is represented by a Glauber coherent state α ( t) L, where α ( t) represents the time-varying magnitude of the pump field. The atomic levels are labeled a, b, and c and A A A form a Λ system. The optical cavity may contain either zero or one photon tuned, represented by the photon number states 0 C and 1 C. The total state (or wavevector) of the system is represented as where, ψ = φ φ φ = φ φ φ (1) L A C L A C φ is the state of the pump field, φ is the state of the atom, φ is the state of L A C the cavity, and represents the tensor product (usually omitted for brevity). We note that the pump coherent state can be decomposed into photon number states as follows: φ L α( t) = α( ) = (2) 2 n α ( t) 2 t e n L n= 0 n! (At this point, we drop the time depence for simplicity and represent the coherent state as α L, remembering the time-depent nature of α.) Similarly, we represent the atomic state as φ = ca ( t) a A + cb ( t) b + cc ( t) c (3) The cavity state is then represented as 149

163 150 We require c ( t) + c ( t) + c ( t) = 1 and a c c φ = ( ) 0 + ( ) 1 (4) c C 0 t c1 t 2 2 c ( t) + c ( t) = 1 (i.e., state vector 0 1 normalization) for all t. We assume the pump is detuned from the a c transition by an angular frequency δ, and the cavity mode represents the frequency detuned from the b c transition by the same amount δ. We take the pump field to be in the coherent state α, the atom to be in the ground state a L A 0 C. The system state can then be written as The coherent state, and the cavity to be in the vacuum state ψ = α a 0 (5) L A C α can be viewed as a decomposition of number states L following a Poisson distribution with mean α and standard deviation α. For large values of α, this distribution roughly resembles a Gaussian distribution with the same mean and standard deviation. The standard deviation is extremely narrow, and the distribution is very nearly symmetric about the peak. For simplicity of analysis, we replace the coherent state with a single number state, i.e., ψ = n a 0 (6) n L A C and we return to the coherent state notation later by taking an appropriate summation over these states. 5.2 Rabi Oscillations When the pump field is applied to the atom, the atom undergoes Rabi oscillations. As discussed in the section entitled The Raman Effect, the atom oscillates between states

164 151 a and b, skipping the intermediate state c. The system state at any time t takes the form ψ ( t) = c ( t) n a 0 + c ( t) n b 1 (7) n a L A C b L A C Using standard approximations relevant to nonlinear optics (the near-resonant excitation, electric dipole, rotating wave, and slowly-varying envelope approximations), the timevarying coefficients for photon number state n can be shown to have the general form c ( t) = cos( Ω t) c ( t) = i sin( Ω t) (8) a R, n b R, n where Ω R, n = 2Ω 0g0 n δ is the Rabi oscillation frequency, g0 = 2µ ba E h is the vacuum Rabi frequency, Ω = µ E 0 0 h is the (complex) Rabi oscillation frequency, and µ E ba is a matrix element of the electric dipole interaction Hamiltonian, consisting of the electric dipole moment µ and the pump field envelope E. (Note that c (0) = 1 and ab a c (0) 0 b =, indicating the atom is initially in the ground state.) For large α, the coherent state resembles a Gaussian distribution of number states with mean α and standard deviation α. The number states n that contribute most to the coherent summation are those with values near n = α, i.e., n = α(1 ± α). Taking the Taylor series expansion of α (i.e., the additional field strength factor, not the standard deviation), we find that 2Ω0g0 2Ω0g0 α Ω R, α (1 ± α ) = α(1 ± α) α 1± δ δ 2 Roughly speaking, the final term in Equation (9) will have equal positive and negative (9) contributions, since the number states are distributed more or less symmetrically about α. Thus, the overall Rabi frequency is given by 2Ω g δ 0 0 Ω R = NP (10)

165 152 where NP α is the average number of photons in the coherent state α. 5.3 Collective Excitation Mode Consider an ensemble of N atoms of the type described above. The ensemble has the state vector where ( ) ψ = α φ φ L φ φ (11) L 1 2 N C φ is the state of atom j. Further, consider that the system is in its ground state, j and that the incident laser is of a low enough intensity that, on average, less than one atom out of the entire ensemble will be excited into a Raman transition. The initial state vector is where we have defined ψ = α a a L a 0 = α A 0 (12) L 1 2 N C L E C A = a a L a (13) E 1 2 N as the ground state of the ensemble. Let us now also define B = a a L b L a (14) j E 1 2 j N as excited state j of the ensemble. If the pulse excites a single atom, we may identify that an atom has been excited from the photon emitted by the stimulated Raman transition; however, we do not know which atom is in the excited state. The ensemble is then in a superposition state; let us define that state as 1 B = ( B E 1 + B E 2 + L + B E N E ) (15) N

166 where the N factor comes from vector normalization. B, then, is the state where E precisely one atom of the ensemble is excited, and all other atoms are in their ground states. We then find that the state of the system after a weak excitation pulse is 1 ψ = CA α A 0 + CB α B 1 (16) L E C L E C N The ensemble then undergoes Rabi oscillations between the A and the B states at a E E Rabi oscillation frequency of factor [20]. Ω R. The extra 5.4 Entanglement Using the Raman Effect N is called the collective enhancement Consider two ensembles of the type described above, numbered 1 and 2. A weak excitation pulse is launched into each ensemble. The output beam paths from the ensembles are combined using a 50/50 beamsplitter; each of the two output ports from the beamsplitter is directed to a photodetector. Call the photodetectors D 1 and D 2. After the excitation pulse, the system is in the state 1 i ψ = (17) 153 ( A B 0 1 B A 1 0 ) ( A A 0 0 B B 1 1 ) (to within a phase factor). If, after a particular excitation pulse, a photon is detected at D 1 but not at D 2, we cannot know with certainty the origin of the photon, so the system is now in state ψ = 1 ( ) 2 A B + B A (18) When the photon is absorbed (annihilated) in the detector, the ensembles remain in the state 1 ψ = ( A B + B A E ) (19) 2

167 154 Thus, when only one detector detects a photon in this setup, the atomic ensembles are macroscopically entangled. 5.5 Photon Storage Using the Raman Effect Consider again an atomic ensemble of the type described above. The ensemble can be used to store a photon. First, let us define two additional ensemble states, namely, 1 N B = b b L b A = b b L a L b (20) E 1 2 N E 1 2 j N N j = 1 The ensemble is first optically pumped into the state B. In the write phase, the pump field (as defined earlier) acts as the write pulse, and the probe provides the photon to be stored. A Raman transition is excited, and the system undergoes a transition from B 1 to A 0. The photon is stored in the ensemble state. Later, in the E C E C read phase, the pump acts as a read pulse; only the atom in the a state sees the pump frequency. A Raman transition is excited, and the system moves from A 0 to B 1, releasing the photon stored in the ensemble state. E C E E C

168 δ c 155 α( t) ω δ ac 0 or 1 ωbc δ b a Figure 50. A three-level system.

169 Chapter 6: Conclusion 6.1 Results and Validity The experimental system described in this text consists of a laser system for exciting Raman gain in neutral rubidium vapor and a detection system observing the results both temporally and spectrally. The experiment itself and the associated detection system have been shown to work effectively to provide the data desired. The experiment has been refined and enhanced in several ways and is now straightforward to operate. Data collection has been streamlined and simplified, and results are cataloged for easy access and for archival. The most interesting result to date produced by the experiment has been the observation of multi-spectral Raman gain in the dual-isotope rubidium vapor induced by a single pump laser. The origins of the spectral lines have been investigated, and a numerical simulation has attributed these lines to Stokes and anti-stokes lines in both rubidium isotopes, as well as to the AC Stark shift. These observations, while striking, are clearly explained by the theory and validate the experimental system as working correctly. For experiments where the multi-spectral gain is a hindrance rather than a beneficial effect, the dual-isotope vapor cell has been replaced with an isotopically pure vapor cell. Promising initial results have been obtained with this cell for the pulsed excitation mode, indicating that the pulsing system and the detection system will both 156

170 157 work properly to achieve this. The pulsed excitation mode allows several interesting experiments to be carried out, including the use of vapor cells as quantum memories and quantum entanglement sources. 6.2 Future Direction The primary future direction of the experiment is to complete measurement and observation of photon correlation in the vapor cell under pulsed excitation. Photon correlation measurements will determine the degree to which entanglement is achieved in the vapor medium. Once macroscopic entanglement is achieved, many further experiments are possible. Two vapor cells may be used in conjunction as a quantum memory. The vapor cells may be used as quantum bits in a quantum computer, or they may be used as elements in a long-distance quantum communications link. Each of these experiments represents a new frontier in optics, clearly predicted by existing theory but yet to be demonstrated experimentally.

171 References [1] Y. Zhu, T. N. Wasserlauf, and P. Sanchez, Effect of optical pumping and Raman scattering on the degenerate four-wave mixing in coherently pumped rubidium atoms, Phys. Rev. A 55, 668 (1997). [2] M. Winter. (2005, February). WebElements Periodic Table (professional edition). [Online]. Available: [3] K. J. R. Rosman and P. D. P. Taylor, Isotopic Compositions of the Elements 1997, Pure Appl. Chem. 70, 217 (1998). [4] A. Heifetz, A. Agarwal, G. C. Cardoso, V. Gopal, P. Kumar, and M. S. Shahriar, "Super efficient absorption filter for quantum memory using atomic ensembles in a vapor," Opt. Commun. 232, 289 (2004). [5] R. W. Boyd, Nonlinear Optics, 2nd ed., San Diego, CA: Academic Press, [6] M. Poelker and P. Kumar, Sodium-Raman laser: direct measurements of the narrow-band Raman gain, Opt. Lett. 17, 399 (1991). [7] J.L. Bowie, J.C. Garrison and R.Y. Chiao, Stimulated Raman gain in a Λ-type atomic system with doubly excited transitions, Phys. Rev. A (2000). [8] Y. Zhu and J. Lin, Sub-Doppler light amplification in a coherently pumped atomic system, Phys. Rev. A 53, 1767 (1996). [9] Y. Zhu, J. Lin and P. Sanchez, Measurement of light amplification in coherently pumped rubidium atoms, Opt. Commun. 128, (1996). 158

172 159 [10] A. E. Kozhekin, K. Mølmer, and E. Polzik, Quantum memory for light, Phys. Rev. A 62, (2000). [11] A. Kuzmich, W. P. Bowen, A. D. Boozer, A. Boca, C. W. Chou, L. M. Duan and H. J. Kimble, Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles, Nature 423, 731 (2003). [12] A.F. Huss, N. Peer, R. Lammegger, E.A. Korsunsky and L. Winholz, Efficient Raman sideband generation in a coherent atomic medium, Phys. Rev. A 63, (2000). [13] L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, Long-distance quantum communication with atomic ensembles and linear optics, Nature 414, 413 (2001). [14] W. Jiang, C. Han, P. Xue, L. M. Duan, G. C. Guo, Nonclassical photon pairs generated from a room-temperature atomic ensemble, Phys. Rev. A 69, (2004). [15] D. N. Matsukevich and A. Kuzmich, Quantum state transfer between matter and light, Science 306, 663 (2004). [16] M. S. Shahriar and P. R. Hemmer, Generation of squeezed states and twin beams via non-degenerate four-wave mixing in a Λ-system, Opt. Commun. 158, 273 (1998). [17] C. H. van der Wal, M. D. Eisaman, A. Andre, R. L. Walsworth, D. F. Phillips, A. S. Zibrov and M. D. Lukin, Atomic memory for correlated photon states, Science 301, 196 (2003).

173 160 [18] M. P. Gordon and P. R. Selvin, A microcontroller-based failsafe for single photon counting modules, Rev. Sci. Instrum. 74, 1150 (2003). [19] The LabVIEW User s Guide. Austin, TX: National Instruments, April [20] [3D] L.M. Duan, J.I. Cirac and P. Zoller, Three-dimensional theory for interaction between atomic ensembles and free-space light, Phys. Rev. A 66, (2002).

174 Appix A: APD Power Supply The APD power supply was fashioned from an ATX-style computer power supply. Such supplies are cheap and readily available. The APD needs a + 5 V DC supply, which the PC power supply provides. The actual voltage measured from the supply in the present experiment under no-load conditions was 5.25 V. The use of a power supply with a built-in power switch is highly recommed. A series of connectors, best referred to as hard drive power connectors, are available from the power supply. (See Figure ff(a).) There is also an ATX power connector, which is inted for connection to the computer motherboard. Two pins on the ATX power connector need to be wired together, namely, pins 13 and 14. (Either soldering or the use of a firmly secured jumper wire will do.) Pin 14 is the PS-ON pin, which the motherboard typically drives low in order to turn the system power on. Pin 13 is a ground pin; wiring pins 13 and 14 together ensures the power supply will provide power. See Figure ff(b), which shows pins 13 and 14 connected. (Whenever the power supply is connected to line voltage and turned on, Pin 9, also called +5VSB, will provide +5 V DC, but maximum draw for that pin is usually between 10 ma and 2 A.) 161

175 Figure 51. Hard drive and ATX power connectors. 162

176 163 Appix B: Fabry-Pérot Cavities B.1 Introduction A Fabry-Pérot cavity, also called a Fabry-Pérot etalon, or an optical resonator, works as a resonator or a wavelength-selective filter. In its simplest configuration, it consists of two planar mirrors oriented parallel to each other and perpicular to a transverse axis. It is appropriate to consider the cavity qualitatively at first to gain an understanding of its operation. A more mathematically rigorous analysis follows. Consider the Fabry-Pérot cavity depicted in Figure 52. The cavity consists of two mirrors, M1 and M2, with air (or vacuum) between them. Imagine a plane wave impinging on M1, traveling along the transverse axis of the cavity (perpicular to M1 and M2). What happens when the wave hits M1? No mirror is perfectly reflective, so let us assume our mirrors have a reflectivity of 99%. That means that 99% of the wave is reflected back in the direction from which it came. Call this reflected wave 1. It also means that 1% of the wave propagates unaffected through M1 and into the cavity. It turns out to be this 1% that is the most interesting. Once the 1% wave hits M2, we have another split: 99% of the 1% wave is reflected back into the cavity, and 1% of the 1% wave is transmitted through M2 and out of the cavity. Call this transmitted wave 1. The wave that is still contained in the cavity propagates back to M1, where 1% of it is transmitted out of the cavity, towards the original source (call it reflected wave 2 ). The remaining 99% is reflected back into the

177 164 cavity, beginning the process once again, giving us transmitted wave 2, reflected wave 3, and so forth. After a long time, the electric field reflected from the cavity towards the source is the sum of many reflected waves, and the electric field transmitted from the cavity along the transverse axis is the sum of many transmitted waves. Here is the crux of the operation of the Fabry-Pérot cavity: If these transmitted waves are all in phase, they will add constructively, producing an output electric field comparable in size to the input field. If they are not perfectly in phase, they will add destructively, and the output electric field will be nearly zero. What determines whether the waves add constructively? In short, constructive interference is achieved when the round-trip length of the cavity is equal to an integral number of wavelengths of the incident field. When the cavity is any other length, the waves will have random phases relative to each other and cancel each other out. Thus, we see the first application of the Fabry-Pérot cavity: a wavelength-selective filter. There are countless other applications of Fabry-Pérot cavities. If one of the cavity mirrors (say, M2) is mounted on an actuator such that it can be moved in a preciselycontrolled manner, the cavity becomes a tunable filter. Attaching feedback electronics to the M2 actuator creates a system that can be used for laser frequency or intensity stabilization. Sweeping the M2 offset linearly with time and recording the cavity output produces an optical spectrum analyzer. Over time, the electric field intensity inside the cavity builds up to a value much greater than the input electric field. Fabry-Pérot cavities provide a way to generate very large electric fields at optical frequencies with reduced

178 165 laser power. Finally, for interferometric physical measurements, Fabry-Pérot cavities provide an effective amplification of the interferometric effect. B.2 Quantitative Analysis We consider the Fabry-Pérot cavity in Figure 52 consisting of two large parallel plane mirrors, M1 and M2, with complex reflectivities ρ 1 and ρ 2 and complex transmissivities τ 1 and τ 2. We allow the mirrors to be infinitely thin, metallic, and non-absorptive. We assume that the mirrors are centered on the z axis of some coordinate system, separated by a distance of L and a medium of index of refraction n, not necessarily unity. We consider a collimated laser beam of some definite cross section impinging perpicularly on M1, i.e., propagating along the transverse axis of the cavity. The beam s cross section is small enough to be entirely reflected by M1 and M2. We allow the beam to have a step-function envelope in time, as though it were switched on instantaneously at some point in time. This laser beam has a definite point of first incidence, but after that point, it appears to be a continuous-wave (CW) beam. We define the complex electric field at the input to the cavity (i.e., just before the first contact with M1) to be monochromatic with amplitude E 0 and free-space wave vector k 0. For convenience, we define k = nk0, τ1 = 1 ρ1, and τ 2 = 1 ρ2, and we proceed with our analysis. We are interested in the electric fields at several points in and around the cavity, namely, at the points R, A, B, and T in Figure 53. The points R and A are is immediately to the left and right of M1, respectively. The points B and T are immediately to the left and right of M2, respectively. Electric fields labeled E Ri are propagating to the left, and

179 166 electric fields labeled E Ti are propagating to the right. Electric fields labeled E Bi are propagating to the right if i is odd and to the left if i is even. E Ai and We have defined the field E 0 to be at the input to the cavity, i.e., right-moving. At M1, the input field is partly reflected and partly transmitted, giving ER 1 = E0ρ1 and EA 1 = E0τ 1. The part of the beam that propagates through the cavity ( E A1 ) acquires a phase ikl e, so ikl ikl EB 1 = EA 1e = E0τ 1e. At M2, E B1 is partly transmitted and partly reflected, giving ikl ikl ET 1 = EB 1τ 2 = E0τ 1τ 2e and EB2 = EB 1ρ2 = E0τ 1ρ2e. The field E B2 now propagates through the cavity to the left, giving ikl i2kl A2 = B2 = 0τ 1ρ2. (For the sake of rigor, E E e E e we note that left-moving fields travel a distance equal to k, since they are moving in the cavity acquires a phase shift of L but have a wave vector of z direction. Thus, each wave propagating through the ikl e, regardless of whether it is left- or right-propagating.) The left-moving field at point A is then partly transmitted and partly reflected, giving E = E τ = E τ ρ e and 2 i2kl R2 A ikl i3kl B3 = A3 = 0τ 1ρ1ρ2, E E e E e i2kl A3 = A2ρ1 = 0τ 1ρ1ρ2. Finally, we note that E E E e i3kl T 3 = B3τ 2 = 0τ 1τ 2ρ1ρ2, and E E E e E = E ρ = E τ ρ ρ e. 2 i3kl B4 B At this point, one can easily see a pattern developing. For example, E E ρ ρ e i2kl T (2 j+ 3) = T (2 j+ 1) 1 2, meaning that ikl i2kl j ET (2 j+ 1) = E0τ 1τ 2e ( ρ1ρ2e ). Similarly, 2 i2kl i2kl j ER(2 j+ 2) = E0τ 1 ρ2e ( ρ1ρ2e ). (All of these expressions hold for j 0, where j is the number of round-trips the beam has traveled through the cavity.) After a long time, the total field transmitted through the cavity ( E ) and the total field reflected from the Fabry-Pérot cavity ( E ) are just the sums of the individual components: R T

180 167 ( ) = = + = = = ) ( j j kl i ikl j j T T T T T T e e E E E E E E E ρ ρ τ τ L ( ) = = + + = + = = ) ( j j kl i kl i j j R R R R R R R e e E E E E E E E E E ρ ρ ρ τ ρ L We can see that the two summations follow a geometric series: 0 1, ( 1) 1 n n a a a = = < We note that 1 1 ρ < and 2 1 ρ < and continue: kl i ikl T e e E E ρ ρ τ τ = + = kl i kl i R e e E E ρ ρ ρ τ ρ We now proceed to view the cavity response in terms of light intensity, where 2 I E. (The proportionality constant deps on the choice of units.) We define exp( ) i ρ ρ φ =, exp( ) i ρ ρ φ =, 1 2 φ φ φ = +, 1 2 ρ ρ ρ = and 1 2 τ τ τ =. First, for simplicity, we note that

181 168 1 ρ ρ e i kl = 2 [ 1 ρ ρ cos(2kl + φ + φ )] + [ ρ ρ sin(2kl + φ] 1 2 = 1 2ρ cos(2kl + φ) + ρ 2 = 1+ ρ 2ρ + 2ρ 2ρ cos(2kl + φ) = (1 ρ) = (1 ρ) = (1 ρ) ρ + 4ρ sin [ 1 cos(2kl + φ) ] 2 1 ( kl + φ / 2) 2 2 [ 1+ (2F / π ) sin ( kl + φ / 2) ] where we have defined F = π ρ /(1 ρ). The parameter F is called the cavity finesse, and its importance will become clear shortly. For now, note that for the usual case where ρ is nearly unity, F is very large ( F >> 1). The intensity of light transmitted through the cavity (in the steady state) is I T = I = E T 2 τ τ e ikl i2kl 1 ρ1ρ2e 2 I τ 1 + F kl (1 ρ) 1 (2 / π ) sin ( φ / 2) I 1 (2 / ) sin ( φ / 2) MAX = F π kl + where IMAX I0 τ (1 ρ) 2 2 = and I E with the same proportionality constant used in all intensity-to-field relations. Figure 54 shows a plot of I T versus L for several values of F ; we proceed to analyze this plot. First of all, note that the plot is periodic, with a period of L = π / k = λ / 2. This is a manifestation of the resonance condition 2L = mλ. For example, assume laser light with λ = 700 nm enters a cavity of length L = 49 µ m. We typically expect φ = 0, meaning that the mirrors don t induce a phase shift upon

182 169 reflection. If the cavity length is changed to L = µ m, the laser light will still resonate. (For cases where φ 0, we may instead think of the cavity as being shortened by an amount φ / 2k. Then, the resonance condition is 2 L = mλ + φ / 2k ; round-trip length changes of an integral number of wavelengths still have no effect on the transmitted light intensity.) The distance λ / 2 is called the free spectral range λ FSR, which is the distance between successive resonance peaks. The index m of a given resonance peak is called the cavity mode or transmission order. The maximum intensity transmitted by the cavity is I MAX. Maximum transmission occurs at resonance. The width of the resonance peak may be measured using the fullwidth at half-maximum (FWHM), which is the wavelength range over which at least half of the maximum intensity is transmitted (for a single resonance peak). We note that the 2 2 intensity reaches half-maximum when 1 + (2 F / π ) sin ( kl + φ / 2) = 2, i.e., when sin( kl + φ / 2) = ± π / 2F. We assume φ = 0, F >> 1, and sin( θ ) θ and find that the half-maximum points are at L = ± π / 2 Fk = ± λ / 4F, giving the FWHM as λ / 2 F = λ / F. This gives the primary definition of the finesse parameter F : it is the FSR ratio of the free spectral range to the resonance peak width. A high-finesse cavity, distinguished by high-reflectivity mirrors, has very sharp resonance peaks and is very sensitive to small changes in either the cavity length or the wavelength of the incident light. A low-finesse cavity, on the other hand, will have broad resonance peaks. The minimum transmitted intensity occurs when + φ =, or when 2 sin ( kl / 2) 1 kl + φ / 2 = ( m + 1/ 2) π, halfway between resonance peaks. The intensity in that case is I T /(1 + (2 F / π ) ) I π / 4F i, a factor of MAX MAX 2 π / 4F smaller than the maximum

183 170 intensity. Thus we have the secondary definition of the finesse, which is a measure of the contrast of the cavity (ratio of maximum to minimum transmission). It is worthwhile to note that Fabry-Pérot cavity parameters are often measured in terms of frequency. In this case, the free spectral range ν FSR = c / 2L, the FWHM ν = ν / F, FSR and the transmitted light intensity at a frequency ν is given by I MAX I T = (2F / π ) sin ( πν / ν + φ / 2) 1 FSR where we have used the fact that kl = 2 πν L / c and ν FSR = c / 2L. The true definition of the cavity free spectral range actually comes from this notation; namely, ν FSR is defined as the maximum frequency range that can be resolved uniquely by a spectrum analyzer. It is clear that the cavity can uniquely resolve frequencies between ν 0 and ν 0 + ν FSR. However, if the spectrum of the input light includes components at, say, both ν + ν / 2 0 FSR and ν ν FSR / 2, a spectrum analyzer tuned to ν / ν FSR will allow both frequencies to resonate. This is similar to the aliasing effect observed when sampling a signal above the Nyquist rate. B.3 Variations on a Theme Many other kinds of Fabry-Pérot cavities are possible. For non-collimated Gaussian beams, instead of planar mirrors, spherical mirrors may be used that match the curvature of the beam phase fronts. The cavity mirrors need not be traditional silvered-glass mirrors; in fact, any reflecting surfaces may be used, such as dielectric interface. (Typically, reflection off a dielectric interface includes a phase shift, so φ 0 in the above derivation.) If the medium between the mirrors has an index of refraction N 1,

184 171 the resonance condition becomes 2 L = mλ / N. The name Fabry-Pérot is usually reserved for a cavity composed of two coaxial mirrors, but an optical cavity may also take other forms. For example, three mirrors arranged in a triangle also function like a cavity; light enters through one mirror, reflects off the second mirror, and reflects off the third mirror back to the first mirror, completing the circuit. Such a cavity is called a ring cavity, and the principles of operation are very similar to those of a Fabry-Pérot cavity. One mirror is chosen as the input mirror, and another mirror is chosen as the output mirror (usually called the output coupler). The output coupler is often of a lower reflectance than the other cavity mirrors; the input mirror is sometimes chosen also to be the output coupler for this reason. Light that leaks out through mirrors other than the output coupler is considered to be a source of loss. One variation that is particularly relevant in the context of this report is the use of distributed Bragg reflectors (DBRs) as mirrors. A DBR consists of alternating parallel layers of two dielectrics (such as indium phosphide and air) with thicknesses chosen to be a quarter-multiple of the wavelength of the incident light, i.e., 2 L = ( m + 1/ 2) λ / N, or L = ( m + 1/ 4) λ / N. Typically, L = (5 / 4) λ / N. The boundaries of each dielectric layer act as a Fabry-Pérot cavity in the reflection mode. Typically, these dielectric boundaries themselves have poor reflectivities, on the order of 30-70%. The dielectric layer acts as a partial mirror, and some or most of the light is transmitted through to the next layer. The next layer in turn acts as a partial mirror, reflecting some of the light. Successive layers continue to act as partial mirrors, and the effective total reflectance of the DBR is equal to the product of the reflectances of the individual partial mirrors (i.e., the cavities formed

185 172 by the individual dielectric layers). DBRs built up in this way can provide extremely high reflectances, well above 99%. Further, they can be fabricated easily using existing semiconductor processes.

186 173 L M1 M2 Figure 52. Schematic of a Fabry-Pérot cavity.

187 174 L A B R Figure 53. Important locations for analyzing cavity resonance.

188 175 I T 0.5 I MAX I MAX F = 5 F = 30 F = (n-1)λ/2 nλ/2 (n+1)λ/2 L-φ/2k Figure 54. Transmitted light intensity for three values of F.

189 176 Appix C: LabVIEW Documentation Vapor Cell Experiment.vi Runs the start-stop and number correlation experiments using the SR430. Version 1.0 ( ) Connector Pane Front Panel Controls and Indicators Experiment type Selects the experiment type. The different experiment types are (where N is the number of cycles run): Raw data. Runs the SR430. The data file contains an Nx(# bins) matrix, where the entire trace of each cycle is in each row. Start-stop. Runs the SR430 and finds the number of bins between the start time (the trigger or start pulse) and the first pulse during the scan (the stop pulse). (The signal input and trigger input of the SR430 should both be wired to the detector output.) Data file

190 177 contains an N-element vector, where each element is the index of the first non-zero bin (starting from 1) for the given cycle. Number correlation. Runs the SR430 and sums the number of pulses over two windows (the write and read pulses). Data file contains an Nx2 matrix, where the first column contains the sums over the first window and the second column contains the sums over the second window. # cycles Number of times (cycles) to run the experiment. Typically, one cycle involves one write/read pulse sequence. Bin width Bin width for the SR430. # Kbins Number of bins to record each cycle (1K-16K). Transferring 1K bins over GPIB takes approximately 60 ms. Transferring 16K bins over GPIB takes approximately 860 ms. (Running one scan takes approximately 270 to 300 ms in addition to the data transfer time.) Total scan time Displays the total SR430 scan time, which is Bin width times # Kbins times After choosing a bin width, entering an approximate time here will change # Kbins to match the nearest correct value. First pulse offset For the Number correlation experiment only. Represents the starting offset of the first "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. First pulse offset (time) For the Number correlation experiment only. Represents the starting offset of the first "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. First pulse duration For the Number correlation experiment only. Represents the number of bins in the first "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. First pulse duration (time) For the Number correlation experiment only. Represents the number of bins in the first "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. Second pulse offset For the Number correlation experiment only. Represents the starting offset of the second "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. Second pulse offset (time) For the Number correlation experiment only. Represents the starting offset of the second "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well.

191 178 Second pulse duration For the Number correlation experiment only. Represents the number of bins in the second "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. Data filename A MATLAB.mat file for storing the output data from the experiment. Load the file in MATLAB using the load command. A two-digit, incrementing number is added to the filename (so, e.g., SS.mat would become SS01.mat). This number is incremented each time the experiment is run, so no data files are overwritten. You can type a filename here or use the browse button (...) to select a filename. In either case, the number will be increased to avoid overwriting any existing files. For example, if you type in the filename SS.mat in a directory that already includes SS01.mat through SS04.mat, the filename will automatically be changed to SS05.mat. Similarly, if you use the browse button to select, say, SS03.mat in the same directory, that file won't be overwritten -- the filename will automatically be changed to SS05.mat. To disable this behavior, choose Manual name. You will still be prompted before any files are overwritten. Browse A MATLAB.mat file for storing the output data from the experiment. Load the file in MATLAB using the load command. A two-digit, incrementing number is added to the filename (so, e.g., SS.mat would become SS01.mat). This number is incremented each time the experiment is run, so no data files are overwritten. You can type a filename here or use the browse button (...) to select a filename. In either case, the number will be increased to avoid overwriting any existing files. For example, if you type in the filename SS.mat in a directory that already includes SS01.mat through SS04.mat, the filename will automatically be changed to SS05.mat. Similarly, if you use the browse button to select, say, SS03.mat in the same directory, that file won't be overwritten -- the filename will automatically be changed to SS05.mat. To disable this behavior, choose Manual name. You will still be prompted before any files are overwritten. Description A description for this particular run of the experiment. Current parameters are added after this description to form the "Full description," which is written to the Readme, log, and data files. Enter a new description here, or choose a previouslyentered description from the drop-down box (the small down arrow to the right of this field). GPIB address Selects the GPIB address of the SR430. Usually set to 8. If the computer has multiple GPIB controllers, use an address of the form X:Y, where X is the controller number (0, 1,...) and Y is the GPIB address on that controller (usually 8). Manual name Normally, the data filename s in an incrementing number (e.g.,

192 179 SS01.mat). After each experiment, the number is incremented (e.g., from SS01.mat to SS02.mat) to avoid overwriting data files. This is the default, recommed behavior. A record of the description and parameters of each file is kept in the files Readme.txt and Start-Stop Log.txt in the same directory as the data file, as well as in the data file itself. To override this filename behavior and force a particular filename, turn on the Manual name switch. (You will be prompted before any data file is overwritten, even if you enable this switch.) Run Starts the experiment running. Most of the front panel will be disabled while the experiment runs. The End now button will be enabled, allowing you to the experiment early. The Run button will show whether the experiment is still running, and the Cycles completed field will show how many cycles have been completed in the current run. End now Ends the current experiment when the current cycle completes. The data, Readme, and log files will still be written correctly (unless an error occurs while writing them). Reinitialize Reinitializes the front panel to its default values. Pressing this button causes a confirmation dialog box to appear. The confirmation dialog box has three buttons: Yes, to confirm reinitialization (same as pressing Enter); No, if the Reinitialize button was pressed by mistake (same as closing the dialog box); and Yes, file/dir too confirms the reinitialization and also reinitializes the output file/directory as at the start of VI execution. This button is primarily inted for use in case the front panel remains partly grayed out after an experiment run completes. Exit Ends execution of the VI. Note that the window will not automatically close. The Exit button is preferred over the stop-sign Abort button on the VI toolbar. If you want to edit this VI, press the Abort button instead. Base data directory Base data directory where data sub-directories reside. The default data directory is <base data directory>\<today's date>. Second pulse duration (time) For the Number correlation experiment only. Represents the number of bins in the first "pulse" window for summing SR430 bins. The number of bins is on the left, and the equivalent time is on the right; entering a number in either field will adjust the corresponding field as well. # records/scan Number of records per scan. Same as "Records/Scan" on the SR430 Mode menu. One experiment cycle sums (averages) this many records together before downloading data from the SR430. Get data Not normally used. Downloads data from the SR430, saves it to the data file, and updates the data filename (if Manual name is not selected). Does not start the SR430 running. This button is not needed after pressing the Run button, as the data is automatically downloaded then. Use the Get data button to download data after pressing the "Start"

193 180 button on the SR430 front panel. (Note: The data downloaded may not be correct if the SR430 is still running when this button is pressed.) Read params Gets settings from the SR430 and makes those the current settings. Full description Contains the full description of the experiment. The full description consists of the Description field, followed by a string containing all of the parameters used for the experiment. The full description is the description written to the data, Readme, and log files. Cycles completed Shows the number of cycles completed so far in the experiment run. You can the experiment early using the End now button. Time stamp Shows the time at which the most recent experiment started. Status Shows the status of the most recently completed experiment, including whether it executed correctly and when it completed. The Status field is blank during the experiment. Readme filename Contains the auto-generated Readme filename. The Readme file contains one line about each experiment run, i.e., data filename and full description. Note that the Readme filename is always Readme.txt in the same directory as the data file and cannot be changed. Log filename Contains the auto-generated log filename. The log file contains several lines of information about the execution of each experiment run, including begin and times and any error encountered. Note that the log filename is always Start-Stop Log.txt in the same directory as the data file and cannot be changed. Bin width (time) Contains the currently selected bin width as a real number with units of time. Always kept in sync with the Bin width ring selector. Overwrite confirmed? True if the user confirmed overwrite of the output file. If false, we should ask for confirmation before running the experiment. Initialize SR430.vi Connector Pane Front Panel

194 181 Controls and Indicators error in (no error) The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. GPIB address status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. SR430 settings

195 182 Bin width # bins (x1k) # records/scan Number of records per scan. Same as "Records/Scan" on the SR430 Mode menu. One experiment cycle sums (averages) this many records together before downloading data from the SR430. trigger level (V) trigger level. Must be within -2.0V <= x <=2.0V trigger slope rising slope TRUE: triggers on rising slope FALSE: triggers on falling slope discriminator slope rising slope TRUE: triggers on rising slope FALSE: triggers on falling slope discriminator level (V) discriminator level. Must be within -0.3V <= x <= 0.3V cursor on cursor on TRUE: display cursor FALSE: do not display cursor error out The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. address out status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed.

196 183 SR430 Run Scan and Get Data.vi Connector Pane Front Panel Controls and Indicators GPIB address error in (no error) The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed.

197 184 code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. Cancel button ref error out The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. Data status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. Data sum address out cancelled? ref out Run Start-Stop Experiment Once.vi

198 185 Connector Pane Front Panel Controls and Indicators error in (no error) The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning.

199 186 GPIB address The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. Cancel button ref error out The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. first non-zero bin index address out cancelled? ref out Write header.vi Connector Pane

200 187 Front Panel Controls and Indicators error in (no error) The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. Output filename

201 188 Readme filename Log filename Time stamp Full description error out The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. Write data and log.vi Writes the experiment data and information to the data and log files. NOTE: This VI will execute even if error in is active. Connector Pane Front Panel

202 189 Controls and Indicators User cancelled? (false) error in (no error) The error in cluster can accept error information wired from VIs previously called. Use this information to decide if any functionality should be bypassed in the event of errors from other VIs. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. status The status boolean is either TRUE (X) for an error, or FALSE (checkmark) for no error or a warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. code The code input identifies the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed. source The source string describes the origin of the error or warning. The pop-up option Explain Error (or Explain Warning) gives more information about the error displayed.